A ray of light enters glass from air at an angle to the normal. Which feature must appear in the correct ray diagram?
Student Revision Notes
Term 3 Physics Quick Review
Grade 10 Advanced Physics - Term 3 EOT Revision Notes
Page mapping used: actual PDF page = textbook page + 5. Example: textbook page 90 -> PDF page 95.
Formula Sheet
- Refraction: n1 sin θ1 = n2 sin θ2; angles are measured from the normal.
- Refractive index: n = c/v, where c = 3.00 × 108 m/s.
- Boundary wave relation: v=fλ; frequency remains constant during refraction.
- Critical angle: For denser to less dense: sin c = n2/n1.
- Thin lens: 1/f = 1/do + 1/di; convex f positive, concave f negative.
- Double slit: λ =xd/L and mλ =xm d/L for bright fringes.
- Single slit: 2x1=2λ L/w; central maximum width is 2x1.
- Diffraction grating: mλ =d sinθ; m=0 central, m=1,2,3... higher orders.
- Relative velocity 1D: va/b + vb/c = va/c.
- Relative velocity 2D: Use vector components, Pythagoras, and tanθ =vy/vx.
Objective-wise Quick Notes
LO01 - Refraction ray diagrams
- Book page(s): 90 | actual PDF page(s): 95
- Exam focus: Describe refraction of light (or a wave) as it crosses the boundary between two different mediums and represent that in a ray diagram.
LO02 - Wave quantities during refraction
- Book page(s): 92-93 | actual PDF page(s): 97-98
- Exam focus: Identify that during refraction, the wavelength and speed of light (or a wave) change but frequency remains the same.
LO03 - Snell's law
- Book page(s): 91-93 | actual PDF page(s): 96-98
- Exam focus: State and apply Snell's law of refraction.
LO04 - Refractive index
- Book page(s): 93, 96 | actual PDF page(s): 98, 101
- Exam focus: Calculate the refractive index of a medium using n=c/v.
LO05 - Critical angle
- Book page(s): 94 | actual PDF page(s): 99
- Exam focus: Define the critical angle as the angle of incidence at which the refracted light ray lies along the boundary of the two mediums.
LO06 - Refraction critical angle and TIR calculations
- Book page(s): 92-94, 96 | actual PDF page(s): 97-99, 101
- Exam focus: Apply the concepts of refraction, critical angle, and total internal reflection to solve numerical problems.
LO07 - Lens parts
- Book page(s): 98-99 | actual PDF page(s): 103-104
- Exam focus: Identify the principal axis, focal points, and focal length of convex or concave lenses.
LO08 - Convex lens ray diagrams
- Book page(s): 98-99, 101 | actual PDF page(s): 103-104, 106
- Exam focus: Draw a ray diagram to find the image of an object at different distances from a convex lens and determine image location and properties.
LO09 - Convex lens magnifier
- Book page(s): 99 | actual PDF page(s): 104
- Exam focus: Describe how a convex lens acts as a magnifier.
LO10 - Thin lens equation
- Book page(s): 100-101, 106 | actual PDF page(s): 105-106, 111
- Exam focus: Apply the thin lens equation to calculate image distance, object distance, or focal length using appropriate algebraic signs.
LO11 - Coherent and incoherent light
- Book page(s): 112-113 | actual PDF page(s): 117-118
- Exam focus: Define coherent and incoherent light and explain how coherent light is generated by passing monochromatic light through slits.
LO12 - Double-slit bright and dark fringes
- Book page(s): 113-114 | actual PDF page(s): 118-119
- Exam focus: Explain how bright and dark interference fringes are created in a double-slit investigation with monochromatic light.
LO13 - Double-slit wavelength equation
- Book page(s): 115 | actual PDF page(s): 120
- Exam focus: Apply λ =xd/L to calculate wavelength or an unknown distance in a double-slit investigation.
LO14 - Constructive interference positions
- Book page(s): 115 | actual PDF page(s): 120
- Exam focus: Explain that constructive interference occurs at locations x_m such that mλ =xm d/L, where m=0,1,2...
LO15 - Interference calculations
- Book page(s): 116, 120 | actual PDF page(s): 121, 125
- Exam focus: Apply λ =xd/L and solve problems on interference of light.
LO16 - Thin-film interference
- Book page(s): 117 | actual PDF page(s): 122
- Exam focus: Define and explain thin-film interference.
LO17 - Diffraction of light
- Book page(s): 121-122 | actual PDF page(s): 126-127
- Exam focus: Define diffraction as bending of a wave as it passes the edge of a barrier and explain diffraction of light.
LO18 - Single-slit diffraction calculations
- Book page(s): 123-124, 129 | actual PDF page(s): 128-129, 134
- Exam focus: Apply 2x1=2λ L/w to solve problems on single-slit diffraction.
LO19 - Double-slit vs single-slit comparison
- Book page(s): 121-122 | actual PDF page(s): 126-127
- Exam focus: Compare Young's Double Slit investigation with Single Slit Diffraction regarding spacing, source, width, and intensity.
LO20 - Diffraction grating definitions
- Book page(s): 124-126 | actual PDF page(s): 129-131
- Exam focus: Define a diffraction grating, reflection grating, and grating spectroscope.
LO21 - Diffraction grating equation
- Book page(s): 126 | actual PDF page(s): 131
- Exam focus: Explain constructive interference from a diffraction grating using mλ =d sinθ, where m=1,2,3...
LO22 - Grating spectroscope applications
- Book page(s): 126 | actual PDF page(s): 131
- Exam focus: Explain how a grating spectroscope works and give applications of diffraction gratings such as gemstone analysis.
LO23 - Frame of reference
- Book page(s): 148 | actual PDF page(s): 153
- Exam focus: Define a frame of reference.
LO24 - Relative velocity in one dimension
- Book page(s): 148-149, 152 | actual PDF page(s): 153-154, 157
- Exam focus: Calculate relative velocity using vector addition and subtraction in one dimension: va/b + vb/c = va/c.
LO25 - Relative velocity in two dimensions
- Book page(s): 150-152 | actual PDF page(s): 155-157
- Exam focus: Calculate relative velocity in two dimensions using vector addition/subtraction graphically and arithmetically.
Common Mistakes
- Measuring angles from the surface instead of the normal.
- Forgetting mm, cm, nm, and μm conversions.
- Using n1θ1=n2θ2 instead of Snell's law with sine.
- Forgetting frequency stays constant during refraction.
- Applying total internal reflection from air to glass.
- Using positive focal length for a concave lens.
- Confusing double-slit separation d with single-slit width w.
- Forgetting m=0 is the central maximum.
- Ignoring direction signs in 1D relative velocity.
- Giving a 2D vector answer without direction.
Grade 10 Advanced • pages 90
LO01: Refraction ray diagrams
Describe refraction of light (or a wave) as it crosses the boundary between two different mediums and represent that in a ray diagram.
What is refraction?
The normal in a refraction diagram is drawn
A ray bends towards the normal when entering a new medium. The new medium is probably
A ray bends away from the normal after crossing a boundary. Its speed has
A student measures the angle of incidence from the surface. What is wrong?
If a light ray enters a new medium along the normal, its direction
Which pair of media can produce refraction at a boundary?
When light passes from air into glass at an angle, which statement is correct?
A mirage is mainly caused by:
Draw and label a ray diagram for light entering glass from air at an angle.
Ray bends towards normal.
- 1 mark: boundary shown
- 1 mark: normal drawn perpendicular
- 1 mark: ray bends towards normal in glass
- 1 mark: i and r labelled from normal
Explain why a ray changes direction during refraction.
Speed change causes bending.
- 1 mark: speed changes at boundary
- 1 mark: one side of wavefront changes speed first
- 1 mark: direction bends
Correct this: refraction is the same as reflection.
They are different boundary behaviours.
- 1 mark: reflection stays in original medium
- 1 mark: refraction crosses boundary
- 1 mark: refraction involves speed change
Describe what happens when light enters a new medium along the normal.
Direction unchanged; speed/wavelength may change.
- 1 mark: direction unchanged
- 1 mark: speed may change
- 1 mark: frequency unchanged
Grade 10 Advanced • pages 92-93
LO02: Wave quantities during refraction
Identify that during refraction, the wavelength and speed of light (or a wave) change but frequency remains the same.
During refraction of light, which quantity remains the same?
Light slows down when it enters glass from air. Its wavelength
Light travels from glass to air. Which change is correct?
Why does frequency stay constant at a boundary?
A ray bends towards the normal. Which set of changes is most likely?
Which formula links speed, frequency, and wavelength?
A wave has frequency 5 × 1014 Hz and speed 2 × 108 m/s in a medium. What is its wavelength?
A wave has frequency 6 × 1014 Hz and speed 2.2 × 108 m/s in a medium. What is its wavelength?
Which quantity remains unchanged when light refracts from one medium into another?
Light with wavelength 600 nm in air enters a medium with refractive index n = 1.50. Approximately what is its wavelength in the medium?
A light wave of frequency 6.0 × 1014 Hz travels in glass at 2.0 × 108 m/s. Calculate wavelength.
3.3 × 10-7 m
- 1 mark: λ=v/f
- 1 mark: substitution correct
- 1 mark: 3.3 × 10-7 m
State what happens to speed, wavelength, and frequency from air to denser medium.
Speed and wavelength decrease; frequency constant.
- 1 mark: speed decreases
- 1 mark: wavelength decreases
- 1 mark: frequency unchanged
Use v=fλ to explain why wavelength changes but frequency does not.
Frequency stays fixed; λ follows speed.
- 1 mark: state v=fλ
- 1 mark: frequency set by source
- 1 mark: λ changes when v changes
Water waves have f=4.0 Hz and λ=0.75 m in shallow water. Find speed.
3.0 m/s
- 1 mark: v=fλ
- 1 mark: v=3.0 m/s
Grade 10 Advanced • pages 91-93
LO03: Snell's law
State and apply Snell's law of refraction.
Light travels from n1=1.00 to n2=1.50 with angle of incidence 30°. Find the angle of refraction.
Light travels from n1=1.00 to n2=1.33 with angle of incidence 40°. Find the angle of refraction.
Light travels from n1=1.50 to n2=1.00 with angle of incidence 30°. Find the angle of refraction.
Light travels from n1=1.33 to n2=1.00 with angle of incidence 35°. Find the angle of refraction.
Light travels from n1=1.00 to n2=1.52 with angle of incidence 45°. Find the angle of refraction.
Light travels from n1=1.50 to n2=1.33 with angle of incidence 25°. Find the angle of refraction.
Which equation is Snell's law?
In Snell's law, the angles are measured from the
A ray travels from medium 1 (n = 1.00) into medium 2 (n = 1.50) with θ1 = 30°. What is θ2?
A ray travels from medium 1 (n = 1.00) into medium 2 (n = 1.33) with θ1 = 45°. What is θ2?
State Snell's law and define symbols.
n1 sinθ1=n2 sinθ2
- 1 mark: n1 sinθ1=n2 sinθ2
- 1 mark: n values are refractive indices
- 1 mark: θ1 incident angle from normal
- 1 mark: θ2 refracted angle from normal
Light enters glass n=1.50 from air at i=35.0°. Calculate r.
22.5°
- 1 mark: use Snell's law
- 1 mark: 1.00 sin35 =1.50 sin r
- 1 mark: sin r=0.382
- 1 mark: r=22.5°
Explain why r in glass is smaller than i in air.
Higher n bends ray towards normal.
- 1 mark: glass has larger n
- 1 mark: light slows down
- 1 mark: bends towards normal
Light goes from water n=1.33 to air at i=30.0°. Calculate r.
41.7°
- 1 mark: use Snell's law
- 1 mark: 1.33 sin30=sin r
- 1 mark: sin r=0.665
- 1 mark: r=41.7°
Grade 10 Advanced • pages 93, 96
LO04: Refractive index
Calculate the refractive index of a medium using n=c/v.
The speed of light in a material is 2.00 × 108 m/s. What is its refractive index?
The speed of light in a material is 2.25 × 108 m/s. What is its refractive index?
The speed of light in a material is 1.50 × 108 m/s. What is its refractive index?
The speed of light in a material is 1.24 × 108 m/s. What is its refractive index?
The speed of light in a material is 2.40 × 108 m/s. What is its refractive index?
The speed of light in a material is 1.80 × 108 m/s. What is its refractive index?
Why has refractive index no unit?
A material has n=1.60. What is the speed of light in it?
Light travels in a transparent medium at 2.00 × 10^8 m/s. What is the refractive index of the medium? Use c = 3.00 × 10^8 m/s.
Light travels in a transparent medium at 2.25 × 10^8 m/s. What is the refractive index of the medium? Use c = 3.00 × 10^8 m/s.
Calculate n if light speed in medium is 2.05 × 108 m/s.
1.46
- 1 mark: n=c/v
- 1 mark: substitution
- 1 mark: n=1.46
A medium has n=1.75. Calculate light speed.
1.71 × 108 m/s
- 1 mark: v=c/n
- 1 mark: substitution
- 1 mark: 1.71 × 108 m/s
Explain why diamond n=2.42 bends light more than water n=1.33.
Diamond is more optically dense.
- 1 mark: larger n
- 1 mark: lower speed
- 1 mark: greater bending at boundary
State refractive index in terms of speed.
n=c/v
- 1 mark: ratio of speed in vacuum/air to speed in material
- 1 mark: n=c/v
Grade 10 Advanced • pages 94
LO05: Critical angle
Define the critical angle as the angle of incidence at which the refracted light ray lies along the boundary of the two mediums.
The critical angle is the angle of incidence for which the refracted ray
Critical angle occurs when light travels from
For i greater than the critical angle, the ray undergoes
At the critical angle in glass-air, the refracted angle is
Which angle is the critical angle?
A ray in water reaches water-air boundary at exactly c. It will
Diamond-air has a smaller critical angle than glass-air because diamond has
Which application uses total internal reflection?
A smaller critical angle means that total internal reflection is:
Light travels from a medium with n = 1.50 into a medium with n = 1.00. What is the critical angle?
Define critical angle.
Incident angle giving r=90°
- 1 mark: angle of incidence in denser medium
- 1 mark: refracted ray is 90°/along boundary
State conditions for total internal reflection.
Dense-to-less-dense and i>c.
- 1 mark: higher n to lower n
- 1 mark: i greater than critical angle
Why can TIR not occur from air to glass?
TIR requires high n to low n.
- 1 mark: air lower n
- 1 mark: travels into higher n
- 1 mark: does not bend away to r=90°
At critical angle in glass-air, describe refracted ray.
Along the boundary.
- 1 mark: travels along boundary
- 1 mark: r=90°
Grade 10 Advanced • pages 92-94, 96
LO06: Refraction critical angle and TIR calculations
Apply the concepts of refraction, critical angle, and total internal reflection to solve numerical problems.
Light travels from water (n=1.33) to air (n=1.00). Calculate the critical angle.
Light travels from glass (n=1.50) to air (n=1.00). Calculate the critical angle.
Light travels from diamond (n=2.42) to air (n=1.00). Calculate the critical angle.
Light travels from glass (n=1.50) to water (n=1.33). Calculate the critical angle.
Light travels from flint glass (n=1.62) to air (n=1.00). Calculate the critical angle.
Glass has critical angle 42°. A ray inside glass strikes the boundary at 50°. What happens?
Water-air critical angle is 48.8°. A ray in water strikes at 30°. What happens?
For outside medium air, which material gives the smallest critical angle?
Total internal reflection can occur only when light travels:
Light travels from a medium with n = 1.33 into a medium with n = 1.00. What is the critical angle?
Calculate critical angle for glass n=1.50 to air.
41.8°
- 1 mark: sin c=n2/n1
- 1 mark: sin c=1/1.50
- 1 mark: sin c=0.667
- 1 mark: c=41.8°
Water-air c=48.8°. A ray in water strikes at 55°. Explain.
Total internal reflection.
- 1 mark: from higher to lower n
- 1 mark: 55°>48.8°
- 1 mark: TIR occurs
Fibre core n=1.48, cladding n=1.44. Find c.
76.7°
- 1 mark: sin c=n2/n1
- 1 mark: 1.44/1.48
- 1 mark: 0.973
- 1 mark: c≈76.7°
Why is TIR useful in optical fibres?
It keeps signal in fibre.
- 1 mark: light remains trapped
- 1 mark: repeated TIR guides signal
- 1 mark: low loss
Grade 10 Advanced • pages 98-99
LO07: Lens parts
Identify the principal axis, focal points, and focal length of convex or concave lenses.
The principal axis of a lens is
A convex lens is also called a
A concave lens is also called a
Focal length is the distance from optical centre to
Parallel rays incident on a convex lens emerge
Parallel rays incident on a concave lens emerge
A lens thicker in the middle than at the edges is
A lens thinner in the middle than at the edges is
A convex lens is also called a:
In a ray diagram for a convex lens, a ray parallel to the principal axis refracts:
Label principal axis, optical centre, F and focal length for a convex lens.
Correct lens labels.
- 1 mark: principal axis through centre
- 1 mark: optical centre marked
- 1 mark: F on both sides
- 1 mark: f measured centre to F
Compare convex and concave lenses for parallel rays.
Convex converges; concave diverges.
- 1 mark: convex converges
- 1 mark: convex focus far side
- 1 mark: concave diverges
- 1 mark: concave appears from near focus
Define focal length.
Distance centre to focus.
- 1 mark: distance from optical centre to F
- 1 mark: along principal axis
Explain error if F is drawn above principal axis.
F belongs on the principal axis.
- 1 mark: F lies on principal axis
- 1 mark: at focal distance from centre
Grade 10 Advanced • pages 98-99, 101
LO08: Convex lens ray diagrams
Draw a ray diagram to find the image of an object at different distances from a convex lens and determine image location and properties.
For a convex lens, an object is placed beyond 2F. What image is formed?
For a convex lens, an object is placed at 2F. What image is formed?
For a convex lens, an object is placed between F and 2F. What image is formed?
For a convex lens, an object is placed at F. What image is formed?
For a convex lens, an object is placed inside F. What image is formed?
Which ray rule for a convex lens is correct?
An image that can be projected on a screen is
For a convex lens, an object inside the focal length produces
For a convex lens, an object placed greater than 2f forms an image that is:
For a convex lens, an object placed at 2f forms an image that is:
Draw convex lens image for object beyond 2F and state properties.
Real, inverted, diminished.
- 1 mark: lens/F/2F shown
- 1 mark: parallel ray through F
- 1 mark: central ray straight
- 1 mark: image between F and 2F
- 1 mark: real inverted diminished
State image for object between F and 2F.
Real inverted enlarged.
- 1 mark: real
- 1 mark: inverted
- 1 mark: enlarged beyond 2F
Differentiate real and virtual image.
Real can be projected; virtual cannot.
- 1 mark: real rays meet
- 1 mark: virtual rays appear to meet
- 1 mark: real can be projected; virtual cannot
Object at F for convex lens. Describe image.
Image at infinity.
- 1 mark: emerging rays parallel
- 1 mark: image at infinity
- 1 mark: no nearby screen image
Grade 10 Advanced • pages 99
LO09: Convex lens magnifier
Describe how a convex lens acts as a magnifier.
A convex lens acts as a magnifier when the object is
The image formed by a simple magnifying glass is usually
Why cannot the usual magnified image be projected onto a screen?
A convex lens of focal length 10 cm is used as a magnifier. Which object distance works?
Which lens is used as a simple magnifier?
When a convex lens acts as a magnifier, rays after the lens are usually
If an object moves outside the focal length of a convex magnifying lens, the image can become
The magnifier increases apparent size mainly by producing
For a convex lens, an object placed less than f forms an image that is:
A student wants to magnify a small insect with a single lens. Which lens should be used?
Describe how a convex lens acts as magnifier.
Object inside f gives virtual upright enlarged.
- 1 mark: convex lens used
- 1 mark: object inside focal length
- 1 mark: rays diverge/apparent image
- 1 mark: virtual upright enlarged
f=8.0 cm, object at 5.0 cm. State image type.
Virtual upright enlarged.
- 1 mark: do<f
- 1 mark: virtual
- 1 mark: upright enlarged
Why is concave lens not a simple magnifier?
It reduces real objects.
- 1 mark: concave diverges
- 1 mark: forms reduced virtual image
Give one use and object position for magnifier.
Reading small print; object inside f.
- 1 mark: valid use
- 1 mark: object inside focal length
Grade 10 Advanced • pages 100-101, 106
LO10: Thin lens equation
Apply the thin lens equation to calculate image distance, object distance, or focal length using appropriate algebraic signs.
A convex lens has focal length 10 cm. An object is 30 cm from the lens. Find image distance.
A convex lens has focal length 12 cm. An object is 18 cm from the lens. Find image distance.
A convex lens has focal length 20 cm. An object is 60 cm from the lens. Find image distance.
A convex lens has focal length 15 cm. An object is 45 cm from the lens. Find image distance.
A convex lens has focal length 8 cm. An object is 24 cm from the lens. Find image distance.
A convex lens has focal length 10 cm. An object is 15 cm from the lens. Find image distance.
A concave lens has f=-20 cm and object distance 30 cm. What is image distance?
The thin lens equation is
A convex lens has f = 10 cm. An object is placed 30 cm from the lens. What is the image distance?
A concave lens has f = -10 cm and an object distance do = 20 cm. Which result is correct?
Convex lens f=15 cm, object=45 cm. Find image distance.
22.5 cm
- 1 mark: 1/f=1/do+1/di
- 1 mark: 1/15=1/45+1/di
- 1 mark: 1/di=0.0444
- 1 mark: di=22.5 cm
Concave lens f=-12 cm, object=24 cm. Find image distance.
-8.0 cm
- 1 mark: use thin lens equation
- 1 mark: 1/-12=1/24+1/di
- 1 mark: 1/di=-0.125
- 1 mark: di=-8.0 cm
State sign convention for focal length.
Convex +, concave -.
- 1 mark: convex positive
- 1 mark: concave negative
Real image at 30 cm, object at 20 cm. Find f.
12 cm
- 1 mark: 1/f=1/20+1/30
- 1 mark: 1/f=5/60
- 1 mark: f=12 cm
- 1 mark: unit included
Grade 10 Advanced • pages 112-113
LO11: Coherent and incoherent light
Define coherent and incoherent light and explain how coherent light is generated by passing monochromatic light through slits.
Coherent light sources have
Incoherent light sources have
Why are two slits illuminated by one monochromatic source coherent?
Which setup is best for stable interference?
Monochromatic light means light with
If two sources are incoherent, the interference pattern is
Coherence is most directly linked to
The double-slit sources are coherent because they are
Coherent light sources have:
Monochromatic light means light with:
Define coherent and incoherent light.
Coherent: fixed phase; incoherent: random.
- 1 mark: coherent same frequency/wavelength
- 1 mark: coherent constant phase difference
- 1 mark: incoherent random phase
- 1 mark: no stable fringes for incoherent
Explain coherent light in double slit.
One source feeds both slits.
- 1 mark: one monochromatic source
- 1 mark: passes through two slits
- 1 mark: slits act as coherent secondary sources
Why are two classroom lamps unsuitable?
They are incoherent.
- 1 mark: independent sources
- 1 mark: random phase difference
- 1 mark: fringes unstable/wash out
State two properties of good double-slit light source.
Monochromatic and coherent.
- 1 mark: monochromatic
- 1 mark: coherent
Grade 10 Advanced • pages 113-114
LO12: Double-slit bright and dark fringes
Explain how bright and dark interference fringes are created in a double-slit investigation with monochromatic light.
A bright fringe forms where waves arrive
A dark fringe forms when path difference is
The central fringe is bright because
Crest meeting crest gives
Crest meeting trough gives
Double-slit fringes show that light behaves as
Increasing slit separation d makes fringe spacing
Increasing screen distance L makes fringe spacing
Constructive interference occurs when two waves meet:
Destructive interference in a double-slit pattern corresponds to:
Explain bright fringe creation.
Constructive interference.
- 1 mark: waves overlap
- 1 mark: in phase/path difference mλ
- 1 mark: constructive interference
Explain dark fringe creation.
Destructive interference.
- 1 mark: waves overlap
- 1 mark: out of phase/path difference (m+1/2)λ
- 1 mark: destructive interference
Why is central band bright?
Zero path difference.
- 1 mark: equal path lengths
- 1 mark: zero path difference/in phase
Give two ways to increase fringe spacing.
Increase λ/L or reduce d.
- 1 mark: increase λ or L
- 1 mark: decrease d
Grade 10 Advanced • pages 115
LO13: Double-slit wavelength equation
Apply λ =xd/L to calculate wavelength or an unknown distance in a double-slit investigation.
Fringe spacing x=3.2 mm, slit separation d=0.40 mm, screen distance L=2.0 m. Find wavelength.
Fringe spacing x=4.0 mm, slit separation d=0.25 mm, screen distance L=2.0 m. Find wavelength.
Fringe spacing x=2.5 mm, slit separation d=0.18 mm, screen distance L=1.5 m. Find wavelength.
Fringe spacing x=5.0 mm, slit separation d=0.30 mm, screen distance L=2.5 m. Find wavelength.
Fringe spacing x=1.8 mm, slit separation d=0.15 mm, screen distance L=0.9 m. Find wavelength.
The double-slit equation for wavelength is
In λ =xd/L, x represents
In λ =xd/L, d represents
The first bright fringe is x = 2.0 mm from the center. The slit separation is d = 0.25 mm and L = 1.0 m. What is the wavelength?
The first bright fringe is x = 3.0 mm from the center. The slit separation is d = 0.20 mm and L = 1.2 m. What is the wavelength?
x=3.2 mm, d=0.40 mm, L=2.0 m. Find λ.
6.4 × 10-7 m
- 1 mark: λ =xd/L
- 1 mark: convert x,d to m
- 1 mark: substitute
- 1 mark: λ=6.4 × 10-7 m
Rearrange λ =xd/L for d.
d=λL/x
- 1 mark: λL=xd
- 1 mark: d=λL/x
λ=5.0 × 10-7 m, d=0.25 mm, L=1.5 m. Find x.
3.0 mm
- 1 mark: x=λL/d
- 1 mark: d=2.5 × 10-4 m
- 1 mark: substitute
- 1 mark: x=3.0 mm
How reduce uncertainty in fringe spacing?
Measure many fringes and average.
- 1 mark: measure several fringes
- 1 mark: divide by number of spacings
Grade 10 Advanced • pages 115
LO14: Constructive interference positions
Explain that constructive interference occurs at locations x_m such that mλ =xm d/L, where m=0,1,2...
Constructive interference in double slit occurs when path difference is
The central bright band has order
The first bright fringe has order
The equation for bright fringe position is
If the second bright fringe is 6.0 mm from the centre, fringe spacing is
A pattern has fringe spacing 2.5 mm. The third bright fringe is
For m=2, λ=600 nm, d=0.30 mm, L=1.5 m. x_m is
Bright fringes on the two sides of the central maximum are
In a double-slit experiment, λ = 500 nm, d = 0.25 mm, L = 1.0 m. What is the distance x1 from the central bright fringe to order m = 1?
In a double-slit experiment, λ = 650 nm, d = 0.50 mm, L = 2.0 m. What is the distance x2 from the central bright fringe to order m = 2?
State constructive interference condition and define m.
Path difference=mλ.
- 1 mark: path difference integer wavelength
- 1 mark: mλ =xm d/L
- 1 mark: m=0,1,2... order
Fringe spacing 4.0 mm. Find fifth bright distance.
20 mm
- 1 mark: x_m=mx
- 1 mark: x5=20 mm
Explain why central bright has m=0.
Zero path difference.
- 1 mark: equal distances from slits
- 1 mark: path difference zero
Second bright at 5.4 mm, d=0.20 mm, L=1.8 m. Find λ.
3.0 × 10-7 m
- 1 mark: mλ =xm d/L
- 1 mark: λ=x_m d/(mL)
- 1 mark: substitute m=2
- 1 mark: λ=3.0 × 10-7 m
Grade 10 Advanced • pages 116, 120
LO15: Interference calculations
Apply λ =xd/L and solve problems on interference of light.
A double-slit setup uses λ=630 nm, d=0.35 mm, and L=2.2 m. Find fringe spacing.
A double-slit setup uses λ=560 nm, d=0.28 mm, and L=2.0 m. Find fringe spacing.
A double-slit setup uses λ=650 nm, d=0.40 mm, and L=1.6 m. Find fringe spacing.
A double-slit setup uses λ=480 nm, d=0.24 mm, and L=1.5 m. Find fringe spacing.
A double-slit setup uses λ=600 nm, d=0.50 mm, and L=2.5 m. Find fringe spacing.
If screen distance L is doubled, fringe spacing
If slit separation d is doubled, fringe spacing
Which color gives largest fringe spacing in same setup?
The first bright fringe is x = 1.8 mm from the center. The slit separation is d = 0.30 mm and L = 1.5 m. What is the wavelength?
The first bright fringe is x = 4.0 mm from the center. The slit separation is d = 0.50 mm and L = 2.0 m. What is the wavelength?
λ=630 nm, d=0.35 mm, L=2.2 m. Find x.
4.0 mm
- 1 mark: x=λL/d
- 1 mark: convert units
- 1 mark: substitute
- 1 mark: x≈4.0 mm
x=2.8 mm, L=1.6 m, d=0.32 mm. Find λ.
5.6 × 10-7 m
- 1 mark: λ =xd/L
- 1 mark: convert units
- 1 mark: substitute
- 1 mark: λ=5.6 × 10-7 m
Why measure across 10 fringes?
Improves accuracy.
- 1 mark: larger distance reduces percentage uncertainty
- 1 mark: averaging reduces random error
State two ways to increase fringe spacing.
Increase λ/L or decrease d.
- 1 mark: increase λ or L
- 1 mark: decrease d
Grade 10 Advanced • pages 117
LO16: Thin-film interference
Define and explain thin-film interference.
Thin-film interference is caused by interference of light reflected from
A common example of thin-film interference is
Soap-bubble colors change because
Thin-film interference is evidence that light
In thin films, path difference depends mainly on
Oil films appear colored in white light because
Destructive interference in a thin film happens when reflected waves arrive
Thin-film effects are strongest when thickness is comparable to
Thin-film interference can produce colors because:
A thin soap film shows bright coloured bands under white light. What is the best explanation?
Define thin-film interference.
Interference from surfaces of a thin film.
- 1 mark: interference from waves reflected/transmitted at thin layer surfaces
- 1 mark: due to path difference/phase changes
Why soap bubble shows colors?
Different colors reinforced at different thicknesses.
- 1 mark: white light has many wavelengths
- 1 mark: reflection from top and bottom surfaces
- 1 mark: thickness varies
- 1 mark: different wavelengths interfere
Give two examples of thin-film interference.
Soap bubble and oil film.
- 1 mark: soap bubble/oil film/anti-reflection coating
- 1 mark: second valid example
How does anti-reflection coating reduce glare?
Destructive interference reduces reflection.
- 1 mark: two reflected rays
- 1 mark: coating thickness gives out-of-phase reflection
- 1 mark: destructive interference
Grade 10 Advanced • pages 121-122
LO17: Diffraction of light
Define diffraction as bending of a wave as it passes the edge of a barrier and explain diffraction of light.
Diffraction is
Diffraction is strongest when gap size is
Single-slit diffraction produces
Light diffraction supports the idea that light
If slit width decreases, diffraction pattern becomes
Diffraction of light around a door is not obvious because
A wave spreads into a shadow region after passing an edge. This is
A good light diffraction demonstration uses
Diffraction is best described as:
According to Huygens’ principle, each point on a wavefront acts as:
Define diffraction.
Wave spreading around edges.
- 1 mark: bending/spreading of wave
- 1 mark: around edge/barrier or through gap
Why narrower slit gives wider pattern?
Narrower slit -> wider spread.
- 1 mark: diffraction increases as slit narrows
- 1 mark: strong when width comparable to wavelength
- 1 mark: larger spread angle
Describe single-slit diffraction pattern.
Broad central maximum with weak sides.
- 1 mark: central maximum widest/brightest
- 1 mark: dark bands on sides
- 1 mark: side maxima weaker
Why does diffraction support wave model?
Light behaves as a wave.
- 1 mark: diffraction is wave property
- 1 mark: light spreads/interferes through narrow aperture
Grade 10 Advanced • pages 123-124, 129
LO18: Single-slit diffraction calculations
Apply 2x1=2λ L/w to solve problems on single-slit diffraction.
Light of λ=600 nm passes through a slit of width 0.30 mm. Screen distance is 2.0 m. Find x1.
Light of λ=500 nm passes through a slit of width 0.25 mm. Screen distance is 1.5 m. Find x1.
Light of λ=650 nm passes through a slit of width 0.40 mm. Screen distance is 1.8 m. Find x1.
Light of λ=480 nm passes through a slit of width 0.60 mm. Screen distance is 2.5 m. Find x1.
Light of λ=550 nm passes through a slit of width 0.22 mm. Screen distance is 1.2 m. Find x1.
In 2x1=2λ L/w, 2x1 represents
If slit width w is doubled, central maximum width
If wavelength increases, the diffraction pattern becomes
For single-slit diffraction, λ = 500 nm, L = 2.0 m, and slit width w = 100 μm. What is the width of the central bright band?
For single-slit diffraction, λ = 600 nm, L = 1.5 m, and slit width w = 80 μm. What is the width of the central bright band?
λ=600 nm, w=0.30 mm, L=2.0 m. Find x1 and central width.
x1=4.0 mm, width=8.0 mm
- 1 mark: x1=λL/w
- 1 mark: convert units
- 1 mark: x1=4.0 mm
- 1 mark: central width=2x1
- 1 mark: 8.0 mm
Rearrange 2x1=2λ L/w for w.
w=λL/x1
- 1 mark: cancel 2 or x1=λL/w
- 1 mark: w=λL/x1
What happens if slit becomes narrower?
Pattern widens.
- 1 mark: central maximum widens
- 1 mark: width inversely proportional to w
Central width 10 mm, λ=5.0 × 10-7 m, L=1.5 m. Find w.
1.5 × 10-4 m
- 1 mark: x1=5.0 mm
- 1 mark: w=λL/x1
- 1 mark: substitute
- 1 mark: w=1.5 × 10-4 m
Grade 10 Advanced • pages 121-122
LO19: Double-slit vs single-slit comparison
Compare Young's Double Slit investigation with Single Slit Diffraction regarding spacing, source, width, and intensity.
Compared with double-slit interference, single-slit diffraction has
In ideal double-slit pattern, fringes are
In single-slit diffraction, the central maximum is
Two coherent sources are used in
Single-slit pattern comes from interference from
Both double-slit and single-slit patterns have dark bands due to
Single-slit side bright bands are
A pattern with broad central bright region and weak side regions is likely
A narrower single slit produces a central bright band that is:
Why do dark fringes appear in a light interference pattern?
Compare double-slit and single-slit spacing/source.
Double: two slits equal spacing; single: one slit broad centre.
- 1 mark: double slit uses two coherent slits
- 1 mark: double slit nearly equal spacing
- 1 mark: single slit one aperture
- 1 mark: single slit broad central maximum
Compare intensities.
Single-slit intensity falls outward.
- 1 mark: double slit ideal fringes similar/modulated
- 1 mark: single slit central brightest
- 1 mark: side maxima weaker
Why broad central band suggests single slit?
Broad centre is single-slit feature.
- 1 mark: single slit has broad central maximum
- 1 mark: double slit has evenly spaced fringes
State one similarity.
Both show interference.
- 1 mark: both are wave phenomena
- 1 mark: both have constructive/destructive interference
Grade 10 Advanced • pages 124-126
LO20: Diffraction grating definitions
Define a diffraction grating, reflection grating, and grating spectroscope.
A diffraction grating is
A reflection grating forms spectra using
A grating spectroscope is used to
The spacing d of a grating is distance between
A grating with more lines per mm has
Gratings produce sharp bright lines because
Which device commonly uses a diffraction grating?
Which everyday object can act as a reflection grating?
A diffraction grating is useful because it:
Optical discs can show rainbow colors because their tracks act like:
Define diffraction grating.
Many equally spaced lines/slits.
- 1 mark: many equally spaced slits/lines/grooves
- 1 mark: diffracts light to form spectra/maxima
Define reflection grating and give example.
A reflective grooved grating.
- 1 mark: works by reflecting from grooves
- 1 mark: CD/DVD or reflective spectrometer grating
Define grating spectroscope and purpose.
Instrument for spectra.
- 1 mark: instrument with grating
- 1 mark: separates wavelengths/colors
- 1 mark: observe/measure spectra
500 lines/mm. Calculate grating spacing.
2.0 × 10-6 m
- 1 mark: 500,000 lines/m
- 1 mark: d=1/N
- 1 mark: d=2.0 × 10-6 m
Grade 10 Advanced • pages 126
LO21: Diffraction grating equation
Explain constructive interference from a diffraction grating using mλ =d sinθ, where m=1,2,3...
A grating has d=1.0 × 10-6 m. Light wavelength is 500 nm at order m=1. Find θ.
A grating has d=2.0 × 10-6 m. Light wavelength is 600 nm at order m=1. Find θ.
A grating has d=1.5 × 10-6 m. Light wavelength is 450 nm at order m=2. Find θ.
A grating has d=2.5 × 10-6 m. Light wavelength is 650 nm at order m=1. Find θ.
A grating has d=2.0 × 10-6 m. Light wavelength is 520 nm at order m=2. Find θ.
The grating equation for maxima is
Red light has larger diffraction angle than blue for same grating because red has
Highest possible order when d=2.0 μm and λ=600 nm is
A diffraction grating has 500 lines/mm. For λ = 600 nm and order m = 1, what is the diffraction angle?
A diffraction grating has 600 lines/mm. For λ = 500 nm and order m = 1, what is the diffraction angle?
State grating equation and symbols.
mλ =d sinθ
- 1 mark: mλ =d sinθ
- 1 mark: m order
- 1 mark: λ wavelength
- 1 mark: d spacing and θ angle
d=1.5 × 10-6 m, λ=500 nm. Find first-order angle.
19.5°
- 1 mark: mλ =d sinθ
- 1 mark: sinθ=λ/d
- 1 mark: sinθ=0.333
- 1 mark: θ=19.5°
Why red and blue diffract at different angles?
Red diffracts more.
- 1 mark: different wavelengths
- 1 mark: equation contains λ
- 1 mark: larger λ gives larger θ
Find maximum order for λ=650 nm, d=2.0 × 10-6 m.
m=3
- 1 mark: mλ≤d
- 1 mark: m≤3.08
- 1 mark: highest integer m=3
Grade 10 Advanced • pages 126
LO22: Grating spectroscope applications
Explain how a grating spectroscope works and give applications of diffraction gratings such as gemstone analysis.
A grating spectroscope works by
In a spectroscope, the grating is used to
Gemstones can be analyzed with a spectroscope because materials
An emission spectrum shows
An absorption spectrum shows
A spectroscope slit should be narrow to
A valid use of diffraction gratings is
A gem spectroscope helps identify
A grating spectroscope is designed to:
Optical discs can show rainbow colors because their tracks act like:
Explain how grating spectroscope produces spectrum.
Grating separates wavelengths.
- 1 mark: light through narrow slit/collimator
- 1 mark: hits grating
- 1 mark: different wavelengths construct at different angles
- 1 mark: separate spectral lines observed
Describe use in gemstone analysis.
Spectra identify material.
- 1 mark: pass light through/from gemstone
- 1 mark: observe absorption/transmission lines
- 1 mark: compare with known spectra
Why different elements have different spectral lines?
Characteristic energy levels.
- 1 mark: different energy levels
- 1 mark: emit/absorb specific wavelengths
State two advantages of grating for spectrum measurement.
Sharp measurable lines.
- 1 mark: sharp separated lines/high resolution
- 1 mark: wavelength can be calculated using mλ =d sinθ
Grade 10 Advanced • pages 148
LO23: Frame of reference
Define a frame of reference.
A frame of reference is
A passenger sitting in a moving bus is at rest relative to
The same object can have different velocities because
A car moves east at 20 m/s. A seated passenger's velocity relative to the car is
Relative velocity means
A boat at rest relative to flowing water moves relative to the bank
Why state a reference frame?
Which can be a reference frame?
A frame of reference is:
Relative velocity is useful because:
Define frame of reference.
Viewpoint for measuring motion.
- 1 mark: viewpoint/coordinate system/observer
- 1 mark: used to measure position/velocity
Explain how passenger can be at rest and moving.
Different frames give different velocities.
- 1 mark: at rest relative bus
- 1 mark: moving relative ground
- 1 mark: motion depends on frame
Give two reference frames for boat on river.
Bank and water frames.
- 1 mark: bank/ground
- 1 mark: water/current/boat
Statement 'ball has velocity 5 m/s'. What is missing?
Velocity needs direction and frame.
- 1 mark: direction
- 1 mark: reference frame
Grade 10 Advanced • pages 148-149, 152
LO24: Relative velocity in one dimension
Calculate relative velocity using vector addition and subtraction in one dimension: va/b + vb/c = va/c.
Object A moves 20 m/s east; object B moves 12 m/s east. Taking east positive, find velocity of A relative to B.
Object A moves 20 m/s east; object B moves 12 m/s west. Taking east positive, find velocity of A relative to B.
Object A moves 15 m/s west; object B moves 5 m/s west. Taking east positive, find velocity of A relative to B.
Object A moves 15 m/s west; object B moves 5 m/s east. Taking east positive, find velocity of A relative to B.
Object A moves 30 m/s east; object B moves 30 m/s east. Taking east positive, find velocity of A relative to B.
The one-dimensional relative velocity relation is
A train moves east at 25 m/s. Passenger walks west at 2 m/s relative to train. Passenger velocity relative ground is
Two cars move toward each other at 18 m/s and 22 m/s. Relative speed is
A student walks forward inside a bus at 1.5 m/s relative to the bus. The bus moves forward at 10.0 m/s relative to the ground. What is the student’s velocity relative to the ground?
A student walks forward inside a bus at 2.0 m/s relative to the bus. The bus moves forward at 12.0 m/s relative to the ground. What is the student’s velocity relative to the ground?
Car A east 28 m/s, B east 16 m/s. Find A relative B.
12 m/s east
- 1 mark: east positive
- 1 mark: v=28-16
- 1 mark: 12 m/s east
A east 20 m/s, B west 15 m/s. Find A relative B.
35 m/s east
- 1 mark: vA=+20, vB=-15
- 1 mark: 20-(-15)
- 1 mark: 35 m/s east
Passenger walks forward 1.5 m/s in train east 18 m/s. Find ground velocity.
19.5 m/s east
- 1 mark: add relative velocities
- 1 mark: 1.5+18
- 1 mark: 19.5 m/s east
Why are signs important in 1D relative velocity?
Signs encode direction.
- 1 mark: represent direction
- 1 mark: opposite directions otherwise give wrong result
Grade 10 Advanced • pages 150-152
LO25: Relative velocity in two dimensions
Calculate relative velocity in two dimensions using vector addition/subtraction graphically and arithmetically.
Velocity components are 3 m/s east and 4 m/s north. Find resultant velocity.
Velocity components are 6 m/s east and 8 m/s north. Find resultant velocity.
Velocity components are 5 m/s east and 12 m/s north. Find resultant velocity.
Velocity components are 9 m/s east and 12 m/s north. Find resultant velocity.
Velocity components are 8 m/s east and 15 m/s north. Find resultant velocity.
A plane flies east at 80 m/s in air; wind is 60 m/s north. Ground velocity is
A swimmer heads north at 1.2 m/s; river flows east at 0.9 m/s. Speed relative bank is
In 2D relative velocity, perpendicular components are combined using
A boat moves north at 4.0 m/s relative to water. The river flows east at 3.0 m/s. What is the boat’s speed relative to the ground?
For the same boat (4.0 m/s north, river 3.0 m/s east), what is the direction of the resultant velocity measured east of north?
Plane 120 m/s east and wind 50 m/s north. Find ground velocity.
130 m/s at 22.6° N of E
- 1 mark: components identified
- 1 mark: sqrt(120²+50²)
- 1 mark: 130 m/s
- 1 mark: tanθ=50/120
- 1 mark: 22.6° north of east
Swimmer north 1.6 m/s, current east 1.2 m/s. Find speed/direction.
2.0 m/s at 36.9° E of N
- 1 mark: components east/north
- 1 mark: magnitude sqrt
- 1 mark: 2.0 m/s
- 1 mark: angle using tan
- 1 mark: 36.9° east of north
Describe graphical 2D relative velocity method.
Scale tip-to-tail vectors.
- 1 mark: choose scale
- 1 mark: draw first vector
- 1 mark: draw second tip-to-tail
- 1 mark: measure resultant
Drone 6 m/s east, wind 8 m/s south. Find ground velocity.
10 m/s at 53.1° south of east
- 1 mark: components 6 east 8 south
- 1 mark: magnitude 10 m/s
- 1 mark: angle 53.1°
- 1 mark: south of east