JEE Physics Wave Optics MCQs Set 24

Answer: (b) \( L/c \)

Explanation:
1. \( \tau=L/c \).

Teacher's Note:
1. The wave train lasts for this duration.

Answer: (c) 16 : 1

Explanation:
1. Maximum amplitude \( =a_1+a_2 \), minimum \( =a_1-a_2 \).

Teacher's Note:
1. Intensity is proportional to amplitude squared.

Answer: (b) interference of light

Explanation:
1. The phenomenon depends on film thickness and wavelength.

Teacher's Note:
1. Key relation used: Reflections from the two surfaces of the film interfere.
2. State the governing law first, then substitute; this avoids sign and power-of-ten slips.

Answer: (c) \( n\lambda \)

Explanation:
1. Phase difference \( =2\pi n \).

Teacher's Note:
1. Key relation used: Waves arrive in phase when the path difference is a whole number of wavelengths.
2. After finding the value, test it against the options by a quick order-of-magnitude estimate.

Answer: (c) both produce waves of the same wavelength having constant phase difference

Explanation:
1. Equal amplitude is not required.

Teacher's Note:
1. Key relation used: Constant phase difference with the same frequency defines coherence.
2. Reduce the data to ratios and keep every quantity in SI units before calculating.

Answer: (c) light waves can be polarized

Explanation:
1. Interference and diffraction occur for all waves.

Teacher's Note:
1. Key relation used: Only transverse waves can be polarized.
2. Check the direction of each proportionality (direct or inverse) before substituting numbers.

Answer: (a) 9 : 1

Explanation:
1. \( a\propto\sqrt I \).

Teacher's Note:
1. Key relation used: Amplitude ratio 2 : 1: \( \dfrac{(2+1)^2}{(2-1)^2}=9 \).
2. State the governing law first, then substitute; this avoids sign and power-of-ten slips.

Answer: (a) reflection

Explanation:
1. Interference and diffraction are exclusive to waves.

Teacher's Note:
1. Key relation used: Reflection can be explained by particles as well as waves.
2. After finding the value, test it against the options by a quick order-of-magnitude estimate.

Answer: (b) a single point source

Explanation:
1. Independent sources have random phase changes.

Teacher's Note:
1. Key relation used: Splitting light from a single source gives a fixed phase relation.
2. Reduce the data to ratios and keep every quantity in SI units before calculating.

Answer: (d) interference in which the width of the fringe will be slightly increased

Explanation:
1. \( \lambda_{air}=\lambda_0/\mu \) with \( \mu\approx1.0003 \).

Teacher's Note:
1. Key relation used: Wavelength is slightly larger in vacuum, so fringe width \( \beta=\lambda D/d \) increases.
2. Check the direction of each proportionality (direct or inverse) before substituting numbers.

Answer: (b) energy

Explanation:
1. The average intensity over the pattern equals the sum of the individual intensities.

Teacher's Note:
1. Key relation used: Energy is redistributed from minima to maxima, not created or lost.
2. State the governing law first, then substitute; this avoids sign and power-of-ten slips.

Answer: (c) \( \dfrac{9}{16} \)

Explanation:
1. \( 9:16 \).

Teacher's Note:
1. Key relation used: \( I\propto a^2 \).
2. After finding the value, test it against the options by a quick order-of-magnitude estimate.

Answer: (b) 6

Explanation:
1. Phasor addition with phase difference \( \pi/3 \).

Teacher's Note:
1. Key relation used: \( A=\sqrt{16+9+2\cdot4\cdot3\cos60^\circ}=\sqrt{37}\approx6 \).
2. Reduce the data to ratios and keep every quantity in SI units before calculating.

Answer: (b) \( \pi/2 \)

Explanation:
1. Cosine leads sine by \( \pi/2 \).

Teacher's Note:
1. Key relation used: \( \cos\omega t=\sin(\omega t+\pi/2) \).
2. Check the direction of each proportionality (direct or inverse) before substituting numbers.

Answer: (c) \( \dfrac{\lambda}{2\pi}\phi \)

Explanation:
1. \( \Delta x=\dfrac{\lambda}{2\pi}\phi \).

Teacher's Note:
1. Key relation used: A path difference \( \lambda \) gives phase \( 2\pi \).
2. State the governing law first, then substitute; this avoids sign and power-of-ten slips.

Answer: (c) both phase difference and frequency remain constant

Explanation:
1. A fixed phase relation requires equal frequency.

Teacher's Note:
1. Key relation used: Both conditions are needed for a stationary pattern.
2. After finding the value, test it against the options by a quick order-of-magnitude estimate.

Answer: (d) lags the second by \( \tfrac\pi2 \)

Explanation:
1. Cosine leads sine by \( \pi/2 \).

Teacher's Note:
1. Key relation used: \( y_2=a\sin(\omega t+\pi/2) \) is ahead of \( y_1 \).
2. Reduce the data to ratios and keep every quantity in SI units before calculating.

Answer: (c) 25 : 1

Explanation:
1. Use amplitudes directly.

Teacher's Note:
1. Key relation used: \( \dfrac{(3+2)^2}{(3-2)^2}=25 \).
2. Check the direction of each proportionality (direct or inverse) before substituting numbers.

Answer: (a) all particles on it have the same phase

Explanation:
1. Rays are perpendicular to it.

Teacher's Note:
1. Key relation used: A wavefront is a locus of points of equal phase.
2. State the governing law first, then substitute; this avoids sign and power-of-ten slips.

Answer: (b) perpendicular

Explanation:
1. Wavefront is a surface of constant phase.

Teacher's Note:
1. Key relation used: Rays travel normal to the wavefront in an isotropic medium.
2. After finding the value, test it against the options by a quick order-of-magnitude estimate.

Answer: (c) amplitude

Explanation:
1. Energy flow per unit area.

Teacher's Note:
1. Key relation used: \( I\propto a^2 \).
2. Reduce the data to ratios and keep every quantity in SI units before calculating.

Answer: (b) spherical

Explanation:
1. A line source gives cylindrical wavefronts.

Teacher's Note:
1. Key relation used: Waves spread equally in all directions.
2. Check the direction of each proportionality (direct or inverse) before substituting numbers.

Answer: (c) rectilinear propagation of light

Explanation:
1. It could not explain interference and diffraction.

Teacher's Note:
1. Key relation used: Particles travel in straight lines.
2. State the governing law first, then substitute; this avoids sign and power-of-ten slips.

Answer: (d) diffraction and photoelectric effect

Explanation:
1. Both aspects are needed.

Teacher's Note:
1. Key relation used: Diffraction shows wave nature and the photoelectric effect shows particle nature.
2. After finding the value, test it against the options by a quick order-of-magnitude estimate.