AP Physics 2 Quiz: Double Slit Interference

What this quiz covers

This quiz focuses on Double Slit Interference, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Physics 2.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. They shift toward the uncovered slit because that slit's intensity is greater
2. They remain at the same positions because the path-difference condition is unchanged (correct answer)
3. They disappear entirely because interference requires equal intensities
4. They become closer together because reducing amplitude reduces wavelength

Explanation: This question tests double-slit interference. The positions of bright fringes in double-slit interference are determined by the path difference condition: bright fringes occur where path difference equals integer multiples of the wavelength. This geometric condition depends only on slit separation, wavelength, and screen distance, not on the individual wave amplitudes. Partially covering one slit reduces its amplitude, which decreases the contrast between bright and dark fringes, but doesn't change their positions. Choice C incorrectly assumes that equal intensities are required for any interference to occur. The key insight is that fringe positions depend on geometry and wavelength, not on relative intensities.

Question 2

1. Increase the distance from the slits to the screen (correct answer)
2. Increase the intensity of the laser
3. Decrease the coherence of the light so phases vary randomly
4. Increase the slit separation while keeping everything else fixed

Explanation: This question tests understanding of double-slit interference. In double-slit interference, the spacing between adjacent bright fringes on the screen depends on three factors: wavelength (λ), slit separation (d), and distance to the screen (L). The fringe spacing is proportional to λL/d, meaning it increases when wavelength increases, when screen distance increases, or when slit separation decreases. Since the question asks for increased fringe spacing without calculation, increasing the distance to the screen (choice A) will spread the pattern out, making fringes farther apart. Choice B incorrectly suggests that intensity affects fringe spacing—intensity only changes the brightness of the pattern, not the geometric spacing. The key insight is that fringe spacing is a geometric property determined by the ratio of wavelength and slit separation, scaled by the screen distance.

Question 3

1. A bright fringe because the waves arrive in phase
2. A dark fringe because the waves arrive out of phase (correct answer)
3. A bright fringe because higher intensity shifts fringe locations
4. A dark fringe because each slit forms its own independent pattern

Explanation: This question tests understanding of double-slit interference. When light from two coherent slits travels different distances to reach a point on the screen, the path difference determines whether the waves arrive in phase or out of phase. A path difference of 1.5λ means one wave has traveled exactly one and a half wavelengths more than the other, creating a phase difference of 540° or equivalently 180° (since 360° = one full cycle). When waves arrive 180° out of phase, they interfere destructively, creating a dark fringe. Choice C incorrectly suggests that intensity affects fringe locations, but fringe positions depend only on path difference and wavelength, not intensity. To solve interference problems, remember that path differences of nλ (where n is an integer) produce bright fringes, while path differences of (n + 0.5)λ produce dark fringes.

Question 4

1. The bright and dark fringes largely wash out because the source is not sufficiently coherent (correct answer)
2. The fringe spacing increases because the bulb produces higher intensity light
3. The same sharp fringes remain because each slit acts independently
4. A single central bright region appears because constructive interference requires one slit

Explanation: This question tests double-slit interference. A laser produces highly coherent light, meaning the waves maintain a constant phase relationship, which is essential for stable interference patterns. A filament bulb without a filter emits incoherent white light with many wavelengths and random phase relationships. This lack of coherence causes the interference patterns from different wavelengths and phase relationships to overlap and average out, largely washing out the distinct bright and dark fringes. Choice C incorrectly assumes that slit independence maintains sharp fringes, missing that coherence between slits is crucial. Remember that stable interference patterns require coherent light sources.

Question 5

1. The light from one slit is made more intense than the other slit
2. The path difference is changed to an integer multiple of the wavelength (correct answer)
3. One slit is covered so only a single-slit pattern remains
4. The two slits are illuminated by independent, incoherent light sources

Explanation: This question tests understanding of double-slit interference. In double-slit interference, bright fringes occur when waves from both slits arrive in phase (constructive interference), which happens when the path difference equals an integer multiple of the wavelength (0, λ, 2λ, etc.). Dark fringes occur when waves arrive out of phase (destructive interference), which happens when the path difference equals a half-integer multiple of the wavelength (λ/2, 3λ/2, etc.). The question states that the point currently has a path difference of λ/2, creating a dark fringe. To make this point bright, we need to change the path difference to an integer multiple of the wavelength. Choice A incorrectly suggests that changing intensity affects interference patterns—intensity only affects brightness, not the locations of bright and dark fringes. The key strategy is to remember that interference patterns depend on path difference relative to wavelength, not on the absolute intensity of light.

Question 6

1. A constant phase relationship between waves arriving from the two slits (correct answer)
2. High light intensity so the dark fringes can form
3. Equal slit widths so each slit produces the same single-slit pattern
4. A perfectly reflective screen so interference can occur

Explanation: This question tests understanding of double-slit interference. Double-slit interference requires coherent light sources, meaning the waves from both slits must maintain a constant phase relationship over time. A laser provides coherent light because all photons are in phase, but an ordinary filament bulb emits incoherent light where the phase varies randomly and rapidly. Without coherence, the interference pattern changes too quickly to be observed, resulting in a uniform illumination instead of stable bright and dark fringes. Choice B incorrectly suggests that high intensity is needed for dark fringes—dark fringes form from destructive interference regardless of source intensity. The critical requirement for observable interference is temporal coherence, ensuring that the phase relationship between waves from the two slits remains constant.

Question 7

1. They disappear because the light is not coherent over time (correct answer)
2. They shift outward because the bulb is brighter than the laser
3. They remain sharp because each slit still diffracts light
4. They become darker because interference requires lower intensity

Explanation: This question tests double-slit interference requirements, specifically the need for coherent light. A laser produces coherent light (constant phase relationship), enabling stable interference patterns. A filament bulb emits incoherent light with rapidly changing phase relationships, preventing sustained constructive and destructive interference. Without coherence, the interference pattern disappears, leaving only the overlapping diffraction patterns from each slit. Choice A incorrectly assumes diffraction alone produces sharp fringes, but interference requires coherence. The strategy is to remember that stable interference patterns require coherent sources with fixed phase relationships.

Question 8

1. Adjacent bright fringes become farther apart on the screen (correct answer)
2. Adjacent bright fringes become closer together on the screen
3. Fringe locations stay fixed because only intensity changes
4. Fringes vanish because interference requires large slit separation

Explanation: This question tests understanding of double-slit interference. In double-slit interference, the spacing between adjacent bright fringes is given by Δy = λL/d, where λ is wavelength, L is screen distance, and d is slit separation. When slit separation d is reduced while keeping λ and L constant, the fringe spacing Δy increases inversely with d. This means adjacent bright fringes become farther apart on the screen as the slits move closer together. Choice B incorrectly predicts the opposite effect—this misconception often arises from thinking that closer slits should produce closer fringes. The transferable principle is that fringe spacing is inversely proportional to slit separation: smaller slit separation produces larger fringe spacing.

Question 9

1. Fringe spacing increases because the same angles map to larger distances on the screen (correct answer)
2. Fringe spacing decreases because the light becomes less intense at larger distances
3. Fringe locations are unchanged because each slit produces its own independent pattern
4. Fringes disappear because interference requires the screen to be close to the slits

Explanation: This question tests understanding of double-slit interference. In double-slit interference, the angular positions of bright fringes are determined by the condition that path difference equals integer multiples of the wavelength. When the screen is moved farther away while keeping slit separation and wavelength constant, the angular positions of fringes remain the same, but these same angles now correspond to larger linear distances on the more distant screen. This causes the fringe spacing (distance between adjacent bright fringes) to increase proportionally with screen distance. Choice B incorrectly relates intensity to fringe spacing—while intensity does decrease with distance, this doesn't affect the geometric spacing of fringes. The transferable insight is that fringe spacing scales linearly with screen distance because it's fundamentally an angular phenomenon projected onto the screen.

Question 10

1. A bright fringe forms even if the slits are not coherent
2. A dark fringe forms because the slits act independently with no interference
3. A bright fringe forms because the waves arrive in phase at $P$ (correct answer)
4. A dark fringe forms because the intensity from each slit is reduced at $P$

Explanation: This question tests understanding of double-slit interference. When light from two coherent slits travels to a point on the screen, the waves interfere based on their path difference. A path difference of exactly one wavelength means the waves arrive in phase (crest meets crest), producing constructive interference and a bright fringe. Choice A incorrectly suggests intensity reduction causes dark fringes, but dark fringes result from destructive interference, not reduced individual intensities. The key strategy is to remember that path differences of whole wavelengths (0, λ, 2λ, etc.) produce bright fringes, while half-integer multiples produce dark fringes.

Question 11

1. They shift randomly because brighter light reduces coherence
2. They move farther apart because higher intensity increases interference spacing
3. They disappear because interference occurs only at low intensity
4. They stay at the same positions because geometry sets path differences (correct answer)

Explanation: This question addresses double-slit interference and the role of light intensity. The positions of bright and dark fringes depend solely on the geometry (slit separation, wavelength, screen distance) through the path difference condition. Increasing light intensity makes all fringes brighter but doesn't change their positions, as the constructive and destructive interference conditions remain unchanged. Choice A incorrectly suggests intensity affects fringe spacing, confusing intensity with the geometric factors that determine interference. The principle is that interference pattern positions depend on path differences, not on source brightness.

Question 12

1. A dark fringe because equal paths always cancel
2. A bright fringe because the waves arrive in phase (correct answer)
3. A dark fringe because each slit produces a separate central minimum
4. A bright fringe because intensity alone determines fringe positions

Explanation: This question tests understanding of double-slit interference. At the center of a double-slit pattern, where the path difference equals zero, waves from both slits travel exactly the same distance to reach point U. With zero path difference, the waves arrive perfectly in phase (0° phase difference) and interfere constructively, creating the central bright fringe. This is always the brightest point in the pattern because the waves add with maximum amplitude. Choice A incorrectly claims that equal paths cause cancellation, but waves only cancel when they arrive 180° out of phase. The fundamental principle is that zero path difference always produces maximum constructive interference, regardless of wavelength or slit separation.

Question 13

1. It is an integer multiple of the wavelength (correct answer)
2. It is a half-integer multiple of the wavelength
3. It depends only on the wave speed, not on the geometry
4. It is zero only if the waves have different frequencies

Explanation: This question tests understanding of double-slit interference. In double-slit interference with water waves, constructive interference occurs when wave crests from both sources arrive together, creating large amplitude oscillations. This happens when the path difference between the two sources equals an integer multiple of the wavelength (0, λ, 2λ, etc.). When crests arrive together, they are in phase, which only occurs at these specific path differences. Choice B incorrectly describes the condition for destructive interference, where crests meet troughs. The misconception in choice C is that interference patterns depend on wave properties and geometry, not just wave speed. The key principle is that constructive interference requires waves to arrive in phase, which happens when path differences are integer multiples of the wavelength.

Question 14

1. It increases because each slit produces a wider diffraction pattern
2. It decreases because adjacent bright fringes move closer together (correct answer)
3. It becomes random because interference does not require coherence
4. It stays the same because brightness depends only on source intensity

Explanation: This question examines double-slit interference and how fringe spacing depends on experimental parameters. The fringe spacing formula is Δy = λL/d, where λ is wavelength, L is screen distance, and d is slit separation. When slit separation d increases while λ and L remain constant, the fringe spacing Δy decreases inversely with d, causing adjacent bright fringes to move closer together. Choice A incorrectly confuses single-slit diffraction with double-slit interference spacing. The strategy is to remember that fringe spacing is inversely proportional to slit separation—wider slits produce narrower fringe patterns.

Question 15

1. It becomes bright because the waves return to being in phase (correct answer)
2. It becomes dark because the waves have different amplitudes there
3. It becomes bright only if the source intensity is increased
4. It stays the same because brightness depends only on distance to the screen

Explanation: This problem examines double-slit interference as a function of position on the screen. Starting from the central bright fringe (zero path difference), moving point T upward increases the path difference between the two slits. When the path difference reaches exactly one wavelength, the waves arrive in phase again (after one complete cycle offset), producing constructive interference and a bright fringe. Choice B incorrectly associates different amplitudes with darkness, but equal-amplitude waves can produce either bright or dark fringes depending on phase. The strategy is to track path difference: integer wavelengths yield bright fringes.

Question 16

1. $d$ must be zero because dark fringes occur only at the center
2. $d$ is a half-integer multiple of the wavelength (correct answer)
3. $d$ is an integer multiple of the wavelength
4. $d$ depends only on the intensity of the source, not geometry

Explanation: This problem addresses double-slit interference conditions for dark fringes. Dark fringes occur when waves from the two slits arrive out of phase, causing destructive interference. This happens when the path difference d equals a half-integer multiple of the wavelength: d = (n + 1/2)λ where n = 0, 1, 2, etc. Choice A incorrectly states integer multiples produce dark fringes, but integer multiples actually produce bright fringes. The key insight is that destructive interference requires waves to be half a cycle out of phase, corresponding to half-integer wavelength path differences.

Question 17

1. The added sheet changes the phase of one wave, changing where path differences produce constructive interference (correct answer)
2. The added sheet increases intensity from one slit, moving the bright fringes toward that slit
3. The added sheet makes the two slits act independently, eliminating fixed fringe positions
4. The added sheet changes the screen reflectivity, so maxima occur at different angles

Explanation: This question tests understanding of double-slit interference. When a thin transparent sheet is placed in front of one slit, it increases the optical path length through that slit because light travels slower through the material than through air. This additional optical path length introduces a phase shift for waves passing through that slit relative to the other slit. Since the phase relationship between waves from the two slits has changed, the locations where constructive and destructive interference occur shift on the screen, causing the entire fringe pattern to move. Choice B incorrectly suggests that the sheet changes intensity distribution—while the sheet may slightly reduce intensity through absorption, this doesn't cause fringe shifts. The key concept is that interference patterns depend on the phase difference between waves, which can be altered by changing the optical path length through one path.

Question 18

1. Decrease the slit separation while keeping wavelength and screen distance constant (correct answer)
2. Increase the light intensity equally at both slits while keeping geometry constant
3. Make the two slits emit light that is not coherent with each other
4. Block one slit so the remaining slit produces a single bright region

Explanation: This question tests double-slit interference. The spacing between adjacent bright fringes in a double-slit pattern is given by Δy = λL/d, where λ is wavelength, L is screen distance, and d is slit separation. When slits are moved closer together (d decreases), the fringe spacing Δy increases because they are inversely proportional. This occurs because closer slits create larger angular separations between interference maxima. Choice B incorrectly assumes that light intensity affects fringe spacing, when it only affects fringe brightness. The key strategy is remembering that fringe spacing is inversely proportional to slit separation.

Question 19

1. It decreases because red light has lower frequency and therefore interferes less
2. It increases because the wavelength is larger (correct answer)
3. It stays the same because fringe spacing depends only on intensity
4. It becomes irregular because coherence is unnecessary for interference

Explanation: This question tests double-slit interference. The spacing between adjacent bright fringes is given by Δy = λL/d, where λ is wavelength, L is screen distance, and d is slit separation. Red light has a longer wavelength than blue light (approximately 700 nm vs 450 nm). Since fringe spacing is directly proportional to wavelength, changing from blue to red light increases the fringe spacing. Choice A incorrectly relates frequency to interference strength rather than recognizing that wavelength directly determines fringe spacing. Remember that fringe spacing increases with wavelength: longer wavelengths produce wider-spaced fringes.

Question 20

1. It increases because the same angular separation corresponds to a larger linear separation farther away (correct answer)
2. It decreases because waves spread out less over a longer distance
3. It stays the same because fringe spacing depends only on slit separation
4. It becomes random because interference does not require coherence

Explanation: This question tests double-slit interference. The linear spacing between bright fringes on the screen is given by Δy = λL/d, where L is the screen distance. When screen distance increases, the fringe spacing increases proportionally because the same angular separation between fringes translates to a larger linear separation at a greater distance. This is analogous to how shadows grow larger when you move a screen farther from the light source. Choice B incorrectly suggests that wave spreading affects fringe spacing, when it's actually the geometric projection that matters. Remember that fringe spacing is directly proportional to screen distance.