1True or false
Light from the two halves of the same laser beam is coherent.
Show answer
Answer: True
Both parts come from the same wave, so they keep a constant phase difference.
!Common mistakeSome think coherence needs two separate identical lasers; in fact two separate lasers are generally NOT coherent with each other.
2True or false · ★ Challenge
X-rays and gamma rays can have the same wavelength; they are named differently mainly because of how they are produced.
Show answer
Answer: True
X-rays come from fast electrons hitting a target or electron transitions; gamma rays come from the nucleus. Their ranges overlap.
!Common mistakeSome think the two regions are separated by a sharp wavelength boundary; in fact they overlap.
3True or false
Diffraction changes the direction in which a wave travels, but not its wavelength or frequency.
Show answer
Answer: True
The wave spreads out in the same medium, so its speed, frequency and wavelength stay the same.
!Common mistakeSome confuse diffraction with refraction, where the speed and wavelength do change.
4True or false · ★ Challenge
Measured from minimum to minimum, the central bright band of a single-slit pattern is roughly double the width of any side band.
Show answer
Answer: True
The central maximum stretches from the first minimum on one side (sin θ = −λ/a) to the first on the other (+λ/a); the others lie between consecutive minima only λ/a apart.
!Common mistakeSome think all the bright bands are the same width, as in double-slit fringes.
5Fill in the blank · ★ Challenge
Two coherent sources vibrate in antiphase (phase difference π). At a point where the path difference is zero, there is ______ interference.
Show answer
Answer: destructive
The waves set out half a cycle apart and travel equal distances, so they arrive half a cycle apart and cancel.
!Common mistakeApplying "zero path difference = bright" forgets that this rule assumes the sources are in phase.
6True or false
Just before a vertical soap film bursts, its top looks black because the film there is much thinner than a wavelength.
Show answer
Answer: True
Reflection at the front surface adds a half-wave phase change; with almost no extra path the two reflections cancel for all colours.
!Common mistakeSome think the black part is a hole; the film is still there but so thin that reflections cancel.
7Fill in the blank · ★ Challenge
In an air wedge between two glass plates, moving from one bright fringe to the next corresponds to an increase in the thickness of the air gap of ______.
Show answer
Answer: half a wavelength (λ/2)
The light crosses the gap twice, so a thickness change of λ/2 changes the path by λ.
!Common mistakeAnswering one wavelength forgets that the light goes down AND back up through the gap.
8True or false
Electromagnetic waves are produced by accelerating (oscillating) electric charges, such as electrons moving up and down a radio aerial.
Show answer
Answer: True
A changing current makes changing electric and magnetic fields that spread out as a wave.
!Common mistakeSome think steady currents radiate; only ACCELERATING charges produce electromagnetic waves.
9Multiple choice · ★ Challenge
Which list shows these radiations in order of INCREASING wavelength?
- ARadio, infrared, ultraviolet, gamma
- BUltraviolet, gamma, radio, infrared
- CGamma, ultraviolet, infrared, radio
- DGamma, infrared, ultraviolet, radio
Show answer
Answer: C. Gamma, ultraviolet, infrared, radio
Wavelength increases as frequency decreases: gamma (shortest) → UV → visible → IR → microwaves → radio (longest).
!Common mistakeChoosing "radio … gamma" gives the order of increasing FREQUENCY, the reverse of what was asked.
10True or false
In each order of a grating spectrum, red light is deviated more than violet light.
Show answer
Answer: True
sin θ = nλ/d, so the longest wavelength (red) has the largest angle.
!Common mistakeLearners often carry over the prism result, where violet is bent most; a grating does the opposite.
11Multiple choice · ★ Challenge
Which change lets an astronomical telescope show finer detail (better resolution)?
- AUsing a wider objective lens or mirror
- BUsing an eyepiece of longer focal length
- CObserving through a red filter rather than blue
- DUsing a narrower objective lens or mirror
Show answer
Answer: A. Using a wider objective lens or mirror
θ = 1.22λ/D: a larger aperture D gives a smaller resolvable angle.
!Common mistakeChoosing the eyepiece confuses magnification with resolution; magnifying a blurred image does not show more detail.
12True or false
If one of the two slits in Young's experiment is covered, the interference fringes disappear and only the broad single-slit diffraction pattern remains.
Show answer
Answer: True
Interference needs waves from two sources; one slit alone gives only its own diffraction pattern.
!Common mistakeSome expect the same fringes, only dimmer; without the second source there is nothing to interfere with.
13Fill in the blank · ★ Challenge
A path difference of 3λ/2 between two waves corresponds to a phase difference of ______ rad.
Show answer
Answer: 3π
φ = (2π/λ) × Δ = (2π/λ) × 3λ/2 = 3π.
!Common mistakeAnswering 3λ/2 or 1.5 forgets to multiply by 2π/λ to change a distance into an angle.
14Fill in the blank
Blue light gives a microscope ______ resolving power than red light, because its wavelength is shorter.
Show answer
Answer: better (higher)
The smallest resolvable angle is proportional to λ, so a shorter wavelength resolves finer detail.
!Common mistakeAnswering "lower" reverses the rule; longer wavelengths diffract more and blur fine detail.
15Fill in the blank · ★ Challenge
Using Bragg's law 2d sin θ = nλ, X-rays of wavelength 0.154 nm give a first-order reflection at 22.0° from a set of crystal planes. The spacing of the planes is d = ______ nm.
Show answer
Answer: 0.21
d = nλ/(2 sin θ) = 0.154 ÷ (2 × 0.375) ≈ 0.21 nm.
!Common mistakeForgetting the 2 in 2d sin θ gives 0.41 nm, twice the true spacing.
16Fill in the blank · ★ Challenge
A grating has a slit spacing of 2.0 μm. With light of 650 nm, the total number of bright maxima that can be seen, including the central one, is ______.
Show answer
Answer: 7
nmax = d/λ = 2.0 ÷ 0.65 = 3.08, so n = 3 is the highest order; 3 on each side plus the centre gives 7.
!Common mistakeAnswering 3 forgets the orders on the other side and the central maximum.
17Fill in the blank
In Young's experiment with coherent in-phase slits, the central fringe (zero path difference) is always ______.
Show answer
Answer: bright
Waves from both slits travel equal distances and arrive in phase.
!Common mistakeAnswering "dark" confuses the centre with the first minimum, where the path difference is λ/2.
18Multiple choice
Which statement about electromagnetic waves is correct?
- AThey can be polarised, because they are longitudinal
- BThey need air in order to carry their two fields
- CTheir electric and magnetic fields are parallel
- DThey can be polarised, because they are transverse
Show answer
Answer: D. They can be polarised, because they are transverse
The fields oscillate at right angles to the direction of travel, so the waves are transverse and can be polarised.
!Common mistakeChoosing "longitudinal" is wrong: longitudinal waves (like sound) cannot be polarised at all.
19Multiple choice · ★ Challenge
In Young's experiment, red light of wavelength 700 nm gives fringes 2.1 mm apart. The red light is replaced by green light of 525 nm with the same apparatus. What is the new fringe width?
- A1.6 mm
- B2.8 mm
- C2.1 mm
- D1.2 mm
Show answer
Answer: A. 1.6 mm
β ∝ λ, so β = 2.1 × 525 ÷ 700 ≈ 1.6 mm.
!Common mistakeChoosing 2.8 mm uses the ratio upside down; shorter wavelength gives CLOSER fringes.
20Multiple choice · ★ Challenge
The pupil of the eye is 3.0 mm wide in daylight. Using θ = 1.22λ/D with λ = 550 nm, what is the smallest angle between two points that the eye can resolve?
- A1.8 × 10⁻⁴ rad
- B2.2 × 10⁻¹ rad
- C4.5 × 10³ rad
- D2.2 × 10⁻⁴ rad
Show answer
Answer: D. 2.2 × 10⁻⁴ rad
θ = 1.22 × 550 × 10⁻⁹ ÷ 3.0 × 10⁻³ = 2.2 × 10⁻⁴ rad.
!Common mistakeChoosing 1.8 × 10⁻⁴ rad leaves out the factor 1.22 for a circular opening; 2.2 × 10⁻¹ rad uses D in μm by mistake.
21Multiple choice
According to the Rayleigh criterion, two point sources are just resolved when
- Atheir two central maxima lie exactly on top of each other
- Bone central maximum falls on the other's first minimum
- Ctheir images are separated by one whole fringe width
- Dthe two sources have exactly equal brightness
Show answer
Answer: B. one central maximum falls on the other's first minimum
At that separation there is a small dip in brightness between the two images, so they can just be seen as two.
!Common mistakeChoosing "central maxima overlap" describes two sources seen as one, the opposite of resolved.
22Short answer · ★ Challenge
A learner measures the wavelength of a laser with a double slit, a metre rule and a screen 0.50 m away. She measures the gap between two neighbouring fringes. Suggest three improvements to make her result more accurate.
Show answer
Model answer: Any three: measure across many (e.g. 10 or 20) fringe spacings and divide; increase D (e.g. 2–3 m) to make fringes wider; use a travelling microscope or vernier calliper for d and the fringes; darken the room; repeat and average; measure D from slits to screen with a tape measure.
!Common mistakeSuggesting a brighter laser does not change the fringe spacing; accuracy comes from measuring larger distances.
23Multiple choice
A hologram, like the shiny security image on a bank card, is made by recording
- Aa single ordinary photograph taken through a coloured filter
- Bthe diffraction of white light through a narrow slit
- Cinterference of object light with a reference beam
- Dthe polarisation of light coming from the object
Show answer
Answer: C. interference of object light with a reference beam
Coherent laser light from the object interferes with a reference beam on the film; lighting the pattern later recreates the 3-D wavefront by diffraction.
!Common mistakeChoosing a filtered photograph misses the key idea: a hologram stores phase information through interference, not just brightness.
24Multiple choice · ★ Challenge
An anti-reflection coating on spectacle lenses has refractive index 1.38. What is the minimum thickness for it to cancel reflected light of wavelength 550 nm? (thickness = λ/(4n))
- A138 nm
- B199 nm
- C275 nm
- D100 nm
Show answer
Answer: D. 100 nm
t = λ/(4n) = 550 ÷ (4 × 1.38) ≈ 100 nm, so the extra path 2t is half a wavelength in the coating.
!Common mistakeChoosing 138 nm uses λ/4 in air and forgets that the wavelength in the coating is shorter (λ/n).
25Multiple choice
The colours seen on a soap bubble, or on a thin film of oil on a wet road, are caused by
- Adispersion of white light by a film shaped like a thin prism
- Bdiffraction of light around the oil molecules
- Cabsorption of some colours by the oil or soap
- Dinterference of light reflected from both film surfaces
Show answer
Answer: D. interference of light reflected from both film surfaces
Light reflected from the top and the bottom of the film travels different paths; for each thickness some colours interfere constructively and others destructively.
!Common mistakeChoosing dispersion confuses this with a prism or rainbow, where colours are separated by refraction.
26Short answer · ★ Challenge
Explain why the colours of an oil film on a puddle change as you look at it from different angles, and as the film spreads out.
Show answer
Model answer: The colour seen depends on which wavelengths interfere constructively, which depends on the extra path through the film. This extra path changes with the angle of viewing and with the thickness of the film. As the film spreads it gets thinner, so different wavelengths are reinforced and the colours shift.
!Common mistakeSaying "the oil changes colour" is wrong; the oil is colourless, and the colours come from interference.
27Multiple choice
Which radiation is used in some rural water-treatment units to kill germs, and also causes sunburn?
- AUltraviolet
- BInfrared
- CMicrowaves
- DRadio waves
Show answer
Answer: A. Ultraviolet
UV photons have enough energy to damage the DNA of microbes and of skin cells.
!Common mistakeChoosing infrared confuses feeling warm with damage to cells; infrared photons are too weak to break DNA.
28Short answer · ★ Challenge
When a razor blade is lit by a laser, its shadow on a screen has fine bright and dark bands along its edges instead of a sharp edge. Explain this.
Show answer
Model answer: Light is diffracted at the edge of the blade, so some light spreads into the region of the geometrical shadow and beside it. Waves coming from different parts of the edge region travel different distances and interfere, giving bright and dark bands.
!Common mistakeSaying "the blade reflects light" does not explain the bands; they come from diffraction and interference.
29Short answer · ★ Challenge
Light from the Sun reaches the Earth, but we never hear the noise of explosions on the Sun. Explain this using the nature of the two kinds of wave.
Show answer
Model answer: Light is an electromagnetic wave made of electric and magnetic fields, which need no medium and travel through the vacuum of space. Sound is a mechanical (longitudinal) wave that needs particles to vibrate; space is almost empty, so sound cannot cross it.
!Common mistakeSaying sound is "too slow to arrive" is wrong; it cannot travel through a vacuum at all.
30Multiple choice
X-ray crystallography uses X-rays rather than visible light to study the arrangement of atoms in a crystal because
- AX-rays travel faster through crystals than light
- Bvisible light cannot pass through any solid at all
- CX-ray wavelengths are similar to the spacing of the atoms
- DX-rays are always coherent but light never is
Show answer
Answer: C. X-ray wavelengths are similar to the spacing of the atoms
Diffraction is strong only when the wavelength is comparable to the spacing of the "grating" – about 10⁻¹⁰ m for atoms.
!Common mistakeChoosing "faster" is wrong: all EM waves travel at c in vacuum; it is the wavelength that matters.
31Multiple choice · ★ Challenge
A grating with 400 lines per mm gives the second-order maximum of a lamp line at 26.0°. What is the wavelength?
- A548 nm
- B1100 nm
- C274 nm
- D5.5 × 10⁵ nm
Show answer
Answer: A. 548 nm
d = 1 ÷ 400 000 m = 2.5 × 10⁻⁶ m; λ = d sin θ/n = 2.5 × 10⁻⁶ × 0.438 ÷ 2 = 5.48 × 10⁻⁷ m = 548 nm.
!Common mistakeChoosing 1100 nm forgets to divide by the order n = 2; 5.5 × 10⁵ nm uses d = 1/400 in mm without changing to metres.
32Multiple choice
Water waves of wavelength 2.0 cm pass through a gap in a ripple tank. With which gap width do they spread out the most?
- A9.0 cm
- B2.0 cm
- C20 cm
- D45 cm
Show answer
Answer: B. 2.0 cm
Diffraction is greatest when the gap is about the same size as the wavelength.
!Common mistakeChoosing a wide gap reverses the rule; wide gaps let waves through with little spreading.
33Multiple choice · ★ Challenge
Two loudspeakers on a school stage are driven by the same signal (wavelength 0.68 m). A listener is 3.40 m from one speaker and 4.42 m from the other. What does she hear?
- AA loud sound, as the path difference is 1.5λ
- BA quiet sound, as the path difference is 1.5λ
- CA loud sound, as the path difference is 3λ
- DA quiet sound, as the path difference is 0.75λ
Show answer
Answer: B. A quiet sound, as the path difference is 1.5λ
Path difference = 4.42 − 3.40 = 1.02 m = 1.5 × 0.68 m: an odd number of half wavelengths, so destructive interference.
!Common mistakeChoosing "loud" forgets that 1.5λ is (n + ½)λ, the condition for destructive interference.
34Short answer
Give two practical uses of thin-film interference.
Show answer
Model answer: Any two: anti-reflection coatings on spectacles, camera lenses and solar panels; checking that glass or metal surfaces are flat (air wedges, Newton's rings); measuring very small thicknesses (hair, foil); colour-shifting security marks on banknotes.
!Common mistakeGiving "rainbows" is wrong: rainbows come from refraction and dispersion in raindrops, not thin films.
35Multiple choice · ★ Challenge
Light from a helium–neon laser (632.8 nm) passes through a double slit and makes fringes 3.2 mm apart on a wall 2.5 m away. What is the slit separation?
- A0.079 mm
- B8.1 × 10⁻⁷ mm
- C0.49 mm
- D4.9 mm
Show answer
Answer: C. 0.49 mm
d = λD/β = 632.8 × 10⁻⁹ × 2.5 ÷ 3.2 × 10⁻³ = 4.9 × 10⁻⁴ m = 0.49 mm.
!Common mistakeChoosing 0.079 mm divides λ by βD; rearranging β = λD/d gives d = λD/β.
36Fill in the blank
If the width of a single slit equals the wavelength of the light, the first minimum is at θ = ______°, so the light spreads over the whole space beyond the slit.
Show answer
Answer: 90
sin θ = λ/a = 1, so θ = 90°.
!Common mistakeAnswering 45° assumes θ = λ/a in radians or halves the angle; sin θ = 1 means 90°.
37Multiple choice · ★ Challenge
X-rays of wavelength 0.10 nm and radio waves of wavelength 100 m both travel at c. How many times greater is the frequency of the X-rays?
- A10⁹
- B10⁻¹²
- C10¹¹
- D10¹²
Show answer
Answer: D. 10¹²
f ∝ 1/λ, so the ratio = 100 ÷ (0.10 × 10⁻⁹) = 10¹².
!Common mistakeChoosing 10⁻¹² inverts the ratio; the shorter wavelength has the HIGHER frequency.
38Short answer
Give one source and one use for each of: infrared, gamma rays and radio waves.
Show answer
Model answer: Infrared: hot objects, the Sun, TV remotes – used in remote controls, thermal cameras, cooking. Gamma rays: radioactive nuclei – used to kill cancer cells and to sterilise medical equipment. Radio waves: oscillating currents in aerials – used for radio, TV and mobile communication.
!Common mistakeLearners often give X-rays as the source of gamma rays; gamma rays come from changes in atomic nuclei.
39Short answer · ★ Challenge
Compare the pattern produced by a single slit with that produced by a double slit using the same light.
Show answer
Model answer: Single slit: a very bright central maximum twice as wide as the others, with much dimmer, narrower side maxima whose brightness falls quickly. Double slit: many equally spaced bright fringes of nearly equal width and brightness (inside a broad diffraction envelope).
!Common mistakeSaying both give equally spaced equal fringes ignores the wide, bright central band of the single slit.
40Short answer
Explain why a laser is a better source than a torch for an interference experiment.
Show answer
Model answer: Laser light is coherent (constant phase relationship across the beam) and monochromatic (one wavelength), so the two slits act as coherent sources and give sharp, stable fringes of one colour. A torch gives white, incoherent light from many atoms emitting randomly, so fringes are blurred or need a single slit and filter.
!Common mistakeSaying "the laser is brighter" misses the point; brightness does not make light coherent.
41Multiple choice · ★ Challenge
A screen shows two-slit fringes whose intensity follows I = 4I₀cos²(φ/2). Find the brightness, in terms of I₀, of a spot where the two waves are 2π/3 out of phase.
- A2I₀
- BI₀
- C3I₀
- D0
Show answer
Answer: B. I₀
φ/2 = π/3, cos(π/3) = 0.5, so I = 4I₀ × 0.25 = I₀.
!Common mistakeChoosing 2I₀ uses cos(π/3) without squaring it.
42Multiple choice · ★ Challenge
A slit 0.10 mm wide is lit with 600 nm light, and the pattern falls on a wall 2.0 m beyond it. Find the distance between the middle of the pattern and the SECOND dark band.
- A12 mm
- B48 mm
- C24 mm
- D2.4 mm
Show answer
Answer: C. 24 mm
sin θ = 2λ/a = 2 × 600 × 10⁻⁹ ÷ 1.0 × 10⁻⁴ = 0.012; y = D tan θ ≈ 2.0 × 0.012 = 0.024 m = 24 mm.
!Common mistakeChoosing 12 mm finds the first minimum (n = 1); 48 mm doubles again, as if measuring across both sides.
43Multiple choice
A TV remote control uses infrared of wavelength 940 nm. What is its frequency? (c = 3.0 × 10⁸ m/s)
- A3.2 × 10⁵ Hz
- B2.8 × 10² Hz
- C3.2 × 10¹⁴ Hz
- D3.1 × 10⁻¹⁵ Hz
Show answer
Answer: C. 3.2 × 10¹⁴ Hz
f = c/λ = 3.0 × 10⁸ ÷ 940 × 10⁻⁹ = 3.2 × 10¹⁴ Hz.
!Common mistakeChoosing 3.2 × 10⁵ Hz forgets to change nm into m; 3.1 × 10⁻¹⁵ Hz divides λ by c instead of c by λ.
44Short answer · ★ Challenge
Radio telescopes observing at λ = 21 cm are often tens of metres across, while optical telescopes with mirrors a few metres wide resolve finer detail. Explain why, and estimate how many times wider a radio dish must be than an optical mirror (λ = 550 nm) for the same resolution.
Show answer
Model answer: Resolution depends on λ/D (θ = 1.22λ/D). Radio wavelengths are much longer, so a much larger D is needed for the same θ. Ratio = 0.21 ÷ 550 × 10⁻⁹ ≈ 3.8 × 10⁵, so the dish would have to be about 400 000 times wider; even a 100 m dish resolves less than a small optical telescope.
!Common mistakeSaying radio dishes are large "to collect more power" is only part of it; the main reason here is diffraction at long wavelengths.
45Multiple choice
An AM transmitter sends radio waves of wavelength 400 m. What is their frequency? (c = 3.0 × 10⁸ m/s)
- A750 kHz
- B1.3 kHz
- C1.2 × 10¹¹ Hz
- D7.5 MHz
Show answer
Answer: A. 750 kHz
f = c/λ = 3.0 × 10⁸ ÷ 400 = 7.5 × 10⁵ Hz = 750 kHz.
!Common mistakeChoosing 1.2 × 10¹¹ Hz multiplies c by λ; choosing 7.5 MHz slips a power of ten when changing Hz to MHz.
46Short answer · ★ Challenge
Taking the smallest angle the eye can resolve as 2.2 × 10⁻⁴ rad, estimate the greatest distance at which the two headlights of a car, 1.5 m apart, are seen as two separate lights at night.
Show answer
Model answer: For small angles θ = s/L, so L = s/θ = 1.5 ÷ 2.2 × 10⁻⁴ ≈ 6.8 × 10³ m, about 7 km. Further away the two lights merge into one.
!Common mistakeUsing L = θ/s or forgetting that θ must be in radians gives a nonsense distance.
47Short answer
Explain how a spectroscope with a diffraction grating can identify the elements in a street lamp or a distant star.
Show answer
Model answer: Each element gives out (or absorbs) light only at certain wavelengths, its line spectrum. The grating spreads the light into lines at angles θ with d sin θ = nλ; measuring θ gives each λ. Comparing the measured wavelengths with known spectra (e.g. sodium 589 nm) identifies the elements.
!Common mistakeSaying the colour of the lamp alone identifies the element is unreliable; it is the exact set of line wavelengths that is unique.
48Short answer · ★ Challenge
A radar at an airport sends out a short microwave pulse, and the echo from an aircraft returns 0.20 ms later. How far away is the aircraft? (c = 3.0 × 10⁸ m/s)
Show answer
Model answer: Distance travelled by the pulse = ct = 3.0 × 10⁸ × 0.20 × 10⁻³ = 6.0 × 10⁴ m. This is there and back, so the aircraft is 3.0 × 10⁴ m = 30 km away.
!Common mistakeForgetting to halve the distance gives 60 km; the echo time covers the journey out AND back.
49Short answer
White light passes through a diffraction grating. Describe the pattern on the screen and explain it.
Show answer
Model answer: There is a white central maximum (n = 0), because every wavelength has zero path difference there. On each side there are spectra (first order, second order, …) with violet nearest the centre and red furthest out, because sin θ = nλ/d is larger for longer wavelengths. Higher orders are more spread out and may overlap.
!Common mistakeSaying the centre is coloured or that violet is furthest out reverses the grating rule.
50Short answer · ★ Challenge
Light of wavelength 500 nm passes through two in-phase slits. At point P on the screen the waves from the slits have a phase difference of 7π. Find the path difference, decide whether P is bright or dark, and say which fringe it is.
Show answer
Model answer: Δ = φλ/(2π) = 7π × 500 ÷ 2π = 3.5λ = 1750 nm. 3.5λ is an odd number of half wavelengths, so P is dark. Dark fringes are at 0.5λ, 1.5λ, 2.5λ, 3.5λ, so P is the 4th dark fringe from the centre.
!Common mistakeCalling it the 3rd dark fringe forgets that the first dark fringe is at λ/2, not λ.