CUET UG Physics Booster Test 2 -Diffraction and Polarisation
📌 Answers are locked once submitted — results and explanations appear at the end.
QUESTION 1 OF 20
Choose the correct statements about geometrical shadow regions and diffraction:
1. Diffraction effects are best seen when the obstacle size is much larger than the wavelength
2. Alternate dark and bright regions appear close to the geometrical shadow
3. Light appears to turn around corners into the shadow
4. The finite resolution of optical instruments is limited by diffraction
QUESTION 2 OF 20
In terms of the visibility of diffraction phenomena:
QUESTION 3 OF 20
As the slit width a increases, the spread of the diffracted light and the angular width of the central maximum become respectively:
QUESTION 4 OF 20
In the mathematical treatment of the single slit:
QUESTION 5 OF 20
Consider the statements on the central maximum of single slit diffraction:
1. It occurs at an angle θ = 0
2. It represents a region where the intensity is the weakest
3. It is bounded by the first minima at ± λ/a
4. It is an area of complete destructive interference
QUESTION 6 OF 20
The approximate angular position for the n-th secondary maximum in single slit diffraction is given by:
QUESTION 7 OF 20
A single slit is illuminated with light of wavelength 600 nm. If the first minimum is formed at an angle of 30° (sin 30° = 0.5), what is the width of the slit?
QUESTION 8 OF 20
Identify the incorrect statement regarding the ratio λ/a in diffraction:
QUESTION 9 OF 20
Match List I with List II based on Feynman's discussion:
| List I | List II |
|---|---|
| 1. Double-slit experiment pattern | a. Question of usage |
| 2. Few sources | b. Superposition of single-slit diffraction and double-slit interference |
| 3. Large number of sources | c. Usually called interference |
| 4. Difference between interference and diffraction | d. Word diffraction is more often used |
QUESTION 10 OF 20
In distinguishing interference and diffraction based on source quantity:
QUESTION 11 OF 20
In the razor blade demonstration for viewing a single-slit pattern:
QUESTION 12 OF 20
Choose the correct statements about color fringes in diffraction using white light:
1. Positions of all bands except the central one depend on wavelength
2. Fringes show spectral colors due to wavelength dependence
3. Using a blue filter makes the fringes wider than when using a red filter
4. The central band does not separate into distinct colors like the secondary bands
QUESTION 13 OF 20
Identify the incorrect statement about the transverse nature of light:
QUESTION 14 OF 20
For a wave propagating in the +x direction on a string, the displacement y(x,t) representing a y-polarised wave is given by:
QUESTION 15 OF 20
In a polaroid sheet, the alignment of the long chain molecules and the direction of the transmitted electric vector (pass-axis) are respectively:
QUESTION 16 OF 20
Choose the correct statements regarding the pass-axis of a polaroid:
1. It transmits the component of the electric vector parallel to it
2. It absorbs the electric vector oscillating parallel to the aligned molecules
3. It transmits 100% of the unpolarised incident light
4. It restricts the emerging light's electric vector to a single direction
QUESTION 17 OF 20
An unpolarised light beam of intensity Iin passes through a polariser, and then through an analyzer set at an angle of 60° (cos 60° = 0.5) relative to the polariser's pass axis. What is the final transmitted intensity?
QUESTION 18 OF 20
When three polaroids are arranged such that the first and third are crossed (angle is 90°), and a middle polaroid is placed at an angle θ relative to the first:
QUESTION 19 OF 20
Identify the incorrect statement concerning energy in diffraction:
QUESTION 20 OF 20
Match List I with List II regarding practical uses of polaroids:
| List I | List II |
|---|---|
| 1. Sunglasses | a. Controls intensity of light entering a room |
| 2. 3D movie cameras | b. Uses polarisation for depth perception recording |
| 3. Windowpanes | c. Reduces glare and overall intensity outdoors |
| 4. First polaroid sheet | d. Reduces unpolarised light intensity by half |
Test Complete!
Answer Review
1 Choose the correct statements about geometrical shadow regions and diffraction:
1. Diffraction effects are best seen when the obstacle size is much larger than the wavelength
2. Alternate dark and bright regions appear close to the geometrical shadow
3. Light appears to turn around corners into the shadow
4. The finite resolution of optical instruments is limited by diffraction
�� Diffraction occurs near edges. �� Light bends into shadow regions. �� Optical resolution is diffraction limited.
Statement 2 is correct because diffraction produces alternating bright and dark fringes near the geometrical shadow. Statement 3 is correct because diffraction makes light appear to bend around obstacles and enter shadow regions. Statement 4 is correct because diffraction limits the resolving power of microscopes and telescopes. Statement 1 is incorrect because diffraction is most pronounced when obstacle dimensions are comparable to the wavelength, not much larger.
- �� Statement 1 → Diffraction is strongest when obstacle size ≈ wavelength.
- �� Option A → Contains incorrect Statement 1.
- �� Option C → Contains incorrect Statement 1.
- �� Option D → Contains incorrect Statement 1.
Used
- Option Grouping
Application:
- Evaluate Statements 1, 2, 3 and 4 individually.
Final Logic:
- Only Statements 2, 3 and 4 are correct.
Size ≈ λ → Strong Diffraction
2 In terms of the visibility of diffraction phenomena:
�� Visible light has a very small wavelength. �� Macroscopic objects are much larger than λ. �� Hence diffraction is often less obvious.
Diffraction is observed for all waves, including light. Since visible wavelengths are extremely small compared to everyday objects, diffraction effects are usually weak and difficult to notice. Therefore Option C is correct.
- �� Option A → Diffraction becomes more pronounced as size approaches wavelength.
- �� Option B → Diffraction occurs for light as well.
- �� Option D → Diffraction occurs in vacuum.
Used
- Elimination
Application:
- Remove statements contradicting wave theory.
Final Logic:
- Small wavelength compared to object size makes diffraction less noticeable.
Small λ → Less Visible Diffraction
3 As the slit width a increases, the spread of the diffracted light and the angular width of the central maximum become respectively:
�� Angular width ∝ λ/a. �� Increasing slit width reduces diffraction. �� Central maximum becomes narrower.
The angular width of the central maximum is approximately: 2λ/a As slit width a increases, λ/a decreases. Therefore the diffraction spread decreases and the central maximum becomes narrower.
- �� Option B → Opposite trend.
- �� Option C → Central maximum does not become larger.
- �� Option D → Diffraction spread does not increase.
Used
- Formula Recall
Application:
- Use width ∝ λ/a.
Final Logic:
- Larger slit width gives smaller diffraction spread.
Big Slit → Small Spread
4 In the mathematical treatment of the single slit:
�� Huygens principle is used. �� Secondary sources are coherent. �� They start in phase.
According to Huygens' principle, every point on the incident wavefront acts as a secondary source. Since all points belong to the same wavefront, they are initially in phase and coherent.
- �� Option A → Sources are coherent, not incoherent.
- �� Option C → No initial π phase difference exists.
- �� Option D → Sources are stationary points on the wavefront.
Used
- Conceptual Recall
Application:
- Apply Huygens' principle.
Final Logic:
- Wavefront points act as in-phase secondary sources.
Same Wavefront = Same Phase
5 Consider the statements on the central maximum of single slit diffraction:
1. It occurs at an angle θ = 0
2. It represents a region where the intensity is the weakest
3. It is bounded by the first minima at ± λ/a
4. It is an area of complete destructive interference
�� Central maximum is brightest. �� Located at θ = 0. �� Lies between first minima.
Statement 1 is correct because the central maximum occurs at θ = 0. Statement 3 is correct because it extends between the first minima approximately located at ±λ/a. Statement 2 is incorrect because the central maximum has maximum intensity. Statement 4 is incorrect because it is produced by constructive, not destructive, interference.
- �� Statement 2 → Central maximum is brightest.
- �� Statement 4 → Destructive interference produces minima.
- �� Option A → Contains incorrect Statement 2.
- �� Option C → Contains incorrect Statements 2 and 4.
- �� Option D → Contains incorrect Statements 2 and 4.
Used
- Option Grouping
Application:
- Evaluate each statement independently.
Final Logic:
- Only Statements 1 and 3 are correct.
Central = Brightest at Zero
6 The approximate angular position for the n-th secondary maximum in single slit diffraction is given by:
�� Secondary maxima occur between minima. �� Approximate location uses half-integer values. �� Intensity decreases with order.
The approximate angular position of the nth secondary maximum is: θ ≈ (n + 1/2)λ/a This lies midway between successive minima and gives the approximate location of bright secondary fringes.
- �� Option B → Represents minima condition.
- �� Option C → Not a diffraction maxima formula.
- �� Option D → Uses incorrect parameter D.
Used
- Formula Recall
Application:
- Use standard secondary maxima relation.
Final Logic:
- Half-integer multiples locate secondary maxima.
Maxima → n + 1/2
7 A single slit is illuminated with light of wavelength 600 nm. If the first minimum is formed at an angle of 30° (sin 30° = 0.5), what is the width of the slit?
�� First minimum: a sinθ = λ. �� Substitute values. �� Solve for slit width.
For first minimum: a sinθ = λ a = λ/sinθ = (600 × 10⁻⁹)/0.5 = 1.2 × 10⁻⁶ m Hence Option A is correct.
- �� Option B → Four times smaller than required.
- �� Option C → Ten times smaller.
- �� Option D → Larger than calculated value.
Used
- Substitution
Application:
- Apply the first-minimum condition directly.
Final Logic:
- a = λ/sinθ = 1.2 × 10⁻⁶ m.
First Minimum → a sinθ = λ
8 Identify the incorrect statement regarding the ratio λ/a in diffraction:
�� Ray optics requires diffraction effects to be negligible. �� This occurs when λ/a is very small. �� Statement D reverses the condition.
Ray optics is valid when the wavelength is much smaller than aperture dimensions: λ/a << 1 Statement D incorrectly claims λ/a should be much greater than 1. Therefore it is the incorrect statement.
- �� Option A → Correct relation.
- �� Option B → Correct condition.
- �� Option C → Minima positions depend on λ/a.
Used
- Extreme Word Filter
Application:
- Check the condition required for ray optics.
Final Logic:
- Ray optics requires λ/a << 1, not >> 1.
Ray Optics → λ/a Small
9 Match List I with List II based on Feynman's discussion:
| List I | List II |
|---|---|
| 1. Double-slit experiment pattern | a. Question of usage |
| 2. Few sources | b. Superposition of single-slit diffraction and double-slit interference |
| 3. Large number of sources | c. Usually called interference |
| 4. Difference between interference and diffraction | d. Word diffraction is more often used |
�� Double slit combines interference and diffraction. �� Few sources → interference. �� Many sources → diffraction.
1 → b : Double-slit pattern is a superposition of interference and diffraction. 2 → c : Few coherent sources are usually associated with interference. 3 → d : Large numbers of sources are commonly associated with diffraction. 4 → a : Feynman described the distinction as largely a matter of usage.
- �� Option B → Incorrect matching throughout.
- �� Option C → Reverses the standard associations.
- �� Option D → Does not match Feynman's description.
Used
- Option Grouping
Application:
- Match each concept with its proper description.
Final Logic:
- Only Option A gives all correct pairings.
Few → Interference, Many → Diffraction
10 In distinguishing interference and diffraction based on source quantity:
�� Diffraction involves many secondary sources. �� Interference usually involves a few sources. �� Terminology depends on source distribution.
Diffraction patterns arise due to interference among a large number of secondary wavelets originating from different parts of an aperture or slit. Hence Option B is correct.
- �� Option A → Two sources are typically associated with interference.
- �� Option C → Large numbers of sources are usually termed diffraction.
- �� Option D → Practical distinction exists.
Used
- Conceptual Recall
Application:
- Recall the conventional distinction.
Final Logic:
- Many secondary sources correspond to diffraction.
Many Sources → Diffraction
11 In the razor blade demonstration for viewing a single-slit pattern:
�� Razor blades form a narrow slit. �� The eye observes the diffraction pattern. �� The retina acts as the screen.
In the razor blade experiment, the diffraction pattern formed by the slit is focused onto the retina by the eye lens. Thus, the eye lens acts as the focusing element and the retina acts as the screen where the pattern is observed.
- �� Option A → The blade edges should be parallel, not perpendicular.
- �� Option C → The filament acts as the light source, not the screen.
- �� Option D → Direct sunlight is not recommended because it is too intense and inconvenient.
Used
- Elimination
Application:
- Remove statements inconsistent with the experimental setup.
Final Logic:
- The eye lens focuses the diffraction pattern onto the retina.
Eye Lens → Focus, Retina → Screen
12 Choose the correct statements about color fringes in diffraction using white light:
1. Positions of all bands except the central one depend on wavelength
2. Fringes show spectral colors due to wavelength dependence
3. Using a blue filter makes the fringes wider than when using a red filter
4. The central band does not separate into distinct colors like the secondary bands
�� Diffraction angle depends on wavelength. �� Different wavelengths spread differently. �� Red fringes are wider than blue fringes.
Statement 1 is correct because fringe positions depend on wavelength. Statement 2 is correct because different wavelengths diffract by different amounts, producing spectral colours. Statement 4 is correct because all wavelengths overlap at the central maximum, making it nearly white. Statement 3 is incorrect because blue light has a shorter wavelength and therefore produces narrower fringes than red light.
- �� Statement 3 → Blue fringes are narrower, not wider.
- �� Option B → Contains incorrect Statement 3.
- �� Option C → Contains incorrect Statement 3.
- �� Option D → Contains incorrect Statement 3.
Used
- Option Grouping
Application:
- Evaluate Statements 1, 2, 3 and 4 individually.
Final Logic:
- Only Statements 1, 2 and 4 are correct.
Red Wide, Blue Narrow
13 Identify the incorrect statement about the transverse nature of light:
�� Sound in air is longitudinal. �� Longitudinal waves cannot be polarised. �� Polarisation confirms transverse nature.
Polarisation is a property of transverse waves. Since sound waves in air are longitudinal, they cannot be polarised. Therefore Statement C is incorrect.
- �� Option A → Correct description of electromagnetic waves.
- �� Option B → Correct property of polarisation.
- �� Option D → Correct description of unpolarised light.
Used
- Odd One Out
Application:
- Identify the statement contradicting the concept of polarisation.
Final Logic:
- Longitudinal sound waves cannot be polarised.
No Polarisation for Longitudinal Waves
14 For a wave propagating in the +x direction on a string, the displacement y(x,t) representing a y-polarised wave is given by:
�� Standard wave travelling in +x direction. �� Displacement occurs along y-axis. �� Represents y-polarisation.
A wave travelling in the positive x-direction is represented by: y(x,t) = a sin(kx − ωt) The displacement is along the y-axis while propagation occurs along the x-axis, representing a transverse y-polarised wave.
- �� Option B → Represents motion in the negative x-direction.
- �� Option C → Incorrect wave expression.
- �� Option D → Mathematically equivalent to −sin(kx−ωt), but the standard expression given in NCERT is Option A.
Used
- Formula Recall
Application:
- Use the standard travelling wave equation.
Final Logic:
- Positive x-direction corresponds to kx − ωt.
+x Motion → kx − ωt
15 In a polaroid sheet, the alignment of the long chain molecules and the direction of the transmitted electric vector (pass-axis) are respectively:
�� Molecules are aligned in one direction. �� Parallel electric components are absorbed. �� Perpendicular components are transmitted.
In a polaroid, the long molecular chains are aligned parallel to one another. Electric field components parallel to these chains are absorbed, while the perpendicular component is transmitted. Therefore, the pass-axis is perpendicular to the molecular alignment.
- �� Option A → Pass-axis is not parallel to the molecular alignment.
- �� Option C → Molecular chains are not perpendicular to each other.
- �� Option D → Both relationships are incorrect.
Used
- Conceptual Recall
Application:
- Apply the absorption rule of polaroids.
Final Logic:
- Parallel molecules absorb parallel components and pass perpendicular components.
Molecules Absorb Parallel
16 Choose the correct statements regarding the pass-axis of a polaroid:
1. It transmits the component of the electric vector parallel to it
2. It absorbs the electric vector oscillating parallel to the aligned molecules
3. It transmits 100% of the unpolarised incident light
4. It restricts the emerging light's electric vector to a single direction
�� Polaroids transmit only one component. �� Parallel molecular component is absorbed. �� Emergent light becomes plane polarised.
Statement 1 is correct because the pass-axis transmits the electric field component parallel to it. Statement 2 is correct because components parallel to aligned molecules are absorbed. Statement 4 is correct because the emerging light is restricted to one vibration direction. Statement 3 is incorrect because only half of the intensity of unpolarised light is transmitted.
- �� Statement 3 → A polaroid does not transmit all incident unpolarised light.
- �� Option B → Contains incorrect Statement 3.
- �� Option C → Contains incorrect Statement 3.
- �� Option D → Contains incorrect Statement 3.
Used
- Option Grouping
Application:
- Check each statement independently.
Final Logic:
- Statements 1, 2 and 4 are correct.
Pass One Direction Only
17 An unpolarised light beam of intensity Iin passes through a polariser, and then through an analyzer set at an angle of 60° (cos 60° = 0.5) relative to the polariser's pass axis. What is the final transmitted intensity?
�� First polariser halves intensity. �� Apply Malus' Law. �� Multiply successive transmission factors.
After the first polariser: I₁ = Iin/2 Applying Malus' Law: I = I₁ cos²60° I = (Iin/2) × (1/2)² I = (Iin/2) × 1/4 I = Iin/8 I = 0.125 Iin Hence Option B is correct.
- �� Option A → Ignores initial halving effect.
- �� Option C → Represents intensity after only the first polariser.
- �� Option D → Exceeds physically possible transmitted intensity.
Used
- Substitution
Application:
- Apply intensity reduction step-by-step.
Final Logic:
- (Iin/2) × cos²60° = 0.125 Iin.
Half First, Then Cos²
18 When three polaroids are arranged such that the first and third are crossed (angle is 90°), and a middle polaroid is placed at an angle θ relative to the first:
�� Middle polaroid allows partial transmission. �� Intensity ∝ cos²θ sin²θ. �� Maximum occurs at 45°.
For crossed polaroids with a middle polaroid: I = (I₀/2) cos²θ sin²θ Using: sin²2θ = 4sin²θ cos²θ Intensity is maximum when: 2θ = 90° θ = 45° = π/4 Therefore Option B is correct.
- �� Option A → Middle polaroid allows non-zero transmission.
- �� Option C → Intensity is always less than the initial intensity.
- �� Option D → Depends on angle, not only wavelength.
Used
- Formula Recall
Application:
- Use three-polaroid intensity relation.
Final Logic:
- Maximum transmission occurs at θ = 45°.
Three Polaroids → Max at 45°
19 Identify the incorrect statement concerning energy in diffraction:
�� Energy is conserved. �� Bright and dark regions arise from redistribution. �� No energy is destroyed.
Dark fringes occur because waves interfere destructively at certain points. Energy is not destroyed; it is redistributed to bright regions. Therefore Statement A is incorrect.
- �� Option B → Correct description of redistribution.
- �� Option C → Total energy remains constant.
- �� Option D → Conservation of energy remains valid.
Used
- Extreme Word Filter
Application:
- Focus on the word "destroyed."
Final Logic:
- Interference redistributes energy; it does not destroy it.
Dark ≠ Energy Loss
20 Match List I with List II regarding practical uses of polaroids:
| List I | List II |
|---|---|
| 1. Sunglasses | a. Controls intensity of light entering a room |
| 2. 3D movie cameras | b. Uses polarisation for depth perception recording |
| 3. Windowpanes | c. Reduces glare and overall intensity outdoors |
| 4. First polaroid sheet | d. Reduces unpolarised light intensity by half |
�� Sunglasses reduce glare. �� 3D systems use polarisation. �� First polaroid halves intensity.
1 → c : Polaroid sunglasses reduce glare and excessive light. 2 → b : 3D movie cameras use polarisation to record depth information. 3 → a : Polaroid windowpanes help control light entering rooms. 4 → d : The first polaroid reduces unpolarised light intensity to half. Thus the correct matching is 1-c, 2-b, 3-a, 4-d.
- �� Option B → Incorrectly matches all major applications.
- �� Option C → Incorrect pairing of sunglasses and camera functions.
- �� Option D → Incorrect assignment of first polaroid and sunglasses.
Used
- Option Grouping
Application:
- Match each application with its specific function.
Final Logic:
- Only Option A gives all four correct matches.
Sunglasses–Glare, Camera–3D, Window–Control, First–Half
