Wave Optics

In Young's double slit experiment with slit separation \(d\), fringe width \(\beta\) at distance \(D\) for wavelength \(\lambda\) is:

1. a\(\dfrac{\lambda}{dD}\)
2. b\(\dfrac{\lambda d}{D}\)
3. c\(\dfrac{dD}{\lambda}\)
4. d\(\dfrac{\lambda D}{d}\)

In YDSE, slits are illuminated by light of wavelength \(500\ \text{nm}\); slit separation \(0.5\ \text{mm}\); screen distance \(1\ \text{m}\). Fringe width is:

1. a\(2.5\ \text{mm}\)
2. b\(0.5\ \text{mm}\)
3. c\(1.0\ \text{mm}\)
4. d\(250\ \mu\text{m}\)

The condition for constructive interference in YDSE is path difference equal to:

1. a\(\dfrac{\lambda}{2}\)
2. b\(\dfrac{(2n+1)\lambda}{2}\)
3. c\(n\lambda\)
4. d\(\dfrac{\lambda}{4}\)

Light of wavelength \(600\ \text{nm}\) in air enters a glass block of refractive index \(1.5\). Inside the glass, its wavelength and frequency are (take \(c = 3 \times 10^{8}\ \text{m s}^{-1}\)):

1. a\(900\ \text{nm}\) and \(5 \times 10^{14}\ \text{Hz}\)
2. b\(400\ \text{nm}\) and \(5 \times 10^{14}\ \text{Hz}\)
3. c\(400\ \text{nm}\) and \(3.3 \times 10^{14}\ \text{Hz}\)
4. d\(600\ \text{nm}\) and \(7.5 \times 10^{14}\ \text{Hz}\)

When the slit in a single-slit diffraction experiment is made narrower, the central maximum on the screen:

1. adisappears completely
2. bbecomes narrower
3. cremains the same width
4. dbecomes wider

In Young's double slit experiment with \(d = 1\ \text{mm}\), \(D = 1.5\ \text{m}\), the path difference at a point \(1.5\ \text{mm}\) from the centre is:

1. a\(10^{-3}\ \text{m}\)
2. b\(10^{-6}\ \text{m}\)
3. c\(10^{-9}\ \text{m}\)
4. d\(10^{-4}\ \text{m}\)

Two sources are coherent if they emit waves of:

1. adifferent frequencies but same phase
2. bany two random frequencies
3. cthe same frequency and a constant phase difference
4. ddifferent wavelengths

Two coherent sources of intensity \(I\) each interfere. The maximum intensity at constructive bright fringe is:

1. a\(\sqrt{2}\,I\)
2. b\(2I\)
3. c\(I\)
4. d\(4I\)

Huygens' principle is used to explain:

1. aonly refraction
2. bonly reflection
3. cwave propagation, reflection, refraction, diffraction
4. donly photoelectric effect

Two slits illuminated by \(600\ \text{nm}\) light produce a fringe pattern. If the same slits are illuminated with \(480\ \text{nm}\) light, the fringe width:

1. abecomes 0.64 times its earlier value
2. bbecomes 1.25 times its earlier value
3. cstays the same
4. dbecomes 0.8 times its earlier value

Assertion (A): Diffraction patterns produced by long-wavelength waves are wider than those produced by short-wavelength waves through the same slit.

Reason (R): Angular width of diffraction patterns is proportional to \(\lambda/a\), so longer-wavelength waves produce broader patterns.

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

Assertion (A): In single-slit diffraction, the central maximum is twice as wide as any of the secondary maxima.

Reason (R): Width of central maximum (between first minima) is \(2\lambda/a\), while the spacing of successive minima around any secondary maximum is \(\lambda/a\).

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

Assertion (A): The colours seen when a CD is viewed in white light are due to diffraction.

Reason (R): Diffraction is a general characteristic exhibited by all types of waves, such as sound waves, light waves, water waves and matter waves.

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

Assertion (A): Coherence between two light sources is essential for stable interference.

Reason (R): For a sustained pattern of bright and dark fringes the relative phase between the sources must remain constant in time.

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

1. I. Fringe width is given by \(\beta = \lambda D/d\).
2. II. Bright and dark fringes alternate equidistantly on the screen.
3. III. The central fringe is bright (zero path difference).

Which of the above are CORRECT for YDSE?

1. aOnly I
2. bAll three
3. cOnly II and III
4. dOnly I and II

1. I. The central maximum is the widest of all maxima.
2. II. Minima occur at angles \(\theta \approx n\lambda/a\) for \(n = \pm 1, \pm 2, \pm 3, \ldots\)
3. III. All secondary maxima are equally bright.

Which of the above are CORRECT for diffraction at single slit?

1. aOnly I and II
2. bOnly I
3. cOnly II and III
4. dAll three

1. I. Each point on a wavefront acts as a source of secondary wavelets.
2. II. The new wavefront is the forward envelope of these secondary wavelets.
3. III. Huygens' construction explains both reflection and refraction.

Which of the above are CORRECT regarding Huygens' construction?

1. aOnly I
2. bAll three
3. cOnly I and II
4. dOnly II

1. I. Bright fringes in YDSE occur where the path difference is an integer multiple of the wavelength.
2. II. Dark fringes occur where the path difference is an odd multiple of \(\lambda/2\).

Which of the above are CORRECT regarding interference of light?

1. aOnly I
2. bOnly II
3. cNeither
4. dBoth I and II

Match each item in List I with its corresponding entry in List II:

1. a(i)-S, (ii)-Q, (iii)-R, (iv)-P
2. b(i)-Q, (ii)-P, (iii)-S, (iv)-R
3. c(i)-P, (ii)-Q, (iii)-R, (iv)-S
4. d(i)-R, (ii)-S, (iii)-P, (iv)-Q

Match each situation in List I with the wavefront it gives in List II:

1. a(i)-R, (ii)-S, (iii)-Q, (iv)-P
2. b(i)-S, (ii)-R, (iii)-P, (iv)-Q
3. c(i)-Q, (ii)-S, (iii)-R, (iv)-P
4. d(i)-P, (ii)-Q, (iii)-S, (iv)-R

Match each item in List I with its corresponding entry in List II:

1. a(i)-S, (ii)-R, (iii)-P, (iv)-Q
2. b(i)-Q, (ii)-P, (iii)-S, (iv)-R
3. c(i)-P, (ii)-Q, (iii)-R, (iv)-S
4. d(i)-R, (ii)-S, (iii)-P, (iv)-Q

In YDSE with \(\lambda = 600\ \text{nm}\), \(d = 0.5\ \text{mm}\), \(D = 1.5\ \text{m}\), the fringe width is:

1. a\(0.6\ \text{mm}\)
2. b\(1.8\ \text{mm}\)
3. c\(2.5\ \text{mm}\)
4. d\(0.2\ \text{mm}\)

In YDSE, slit separation \(d = 0.4\ \text{mm}\) and screen distance \(D = 2\ \text{m}\). If the 4th bright fringe is at \(y = 8\ \text{mm}\) from the central fringe, the wavelength of light used is:

1. a\(700\ \text{nm}\)
2. b\(600\ \text{nm}\)
3. c\(500\ \text{nm}\)
4. d\(400\ \text{nm}\)

In YDSE the whole apparatus is immersed in water of refractive index \(\dfrac{4}{3}\). If the fringe width in air is \(1.2\ \text{mm}\), the fringe width in water is:

1. a\(0.9\ \text{mm}\)
2. b\(1.6\ \text{mm}\)
3. c\(1.2\ \text{mm}\)
4. d\(0.3\ \text{mm}\)

In the intensity pattern of Young's double-slit experiment, the central bright fringe corresponds to:

1. afirst dark fringe
2. b\(\lambda/2\) path difference
3. czero path difference
4. dsecond order maximum

A wavefront is refracted at the surface of a denser medium, and the refracted ray bends towards the normal. This is because:

1. afrequency increases
2. bwave amplitude decreases
3. cwavelength stays same
4. dwave speed decreases

Based on the passage, the angular position of the first dark fringe is:

1. a\(\dfrac{\lambda}{d}\)
2. b\(\dfrac{\lambda}{2d}\)
3. c\(\dfrac{2\lambda}{d}\)
4. dzero

Based on the passage, the position of the 3rd bright fringe from the center is:

1. a\(\dfrac{3\lambda D}{d}\)
2. b\(\dfrac{\lambda D}{3d}\)
3. c\(\dfrac{3\lambda D}{2d}\)
4. d\(\dfrac{\lambda D}{d}\)

Based on the passage, if \(D\) is doubled, the fringe width:

1. aquadruples
2. bhalves
3. cstays same
4. ddoubles

Based on the passage, each slit alone would give intensity \(I_{0}\) on the screen. At a point a quarter of a fringe width, \(\dfrac{\lambda D}{4d}\), from the centre of the central bright fringe, the resultant intensity is:

1. a\(4I_{0}\)
2. b\(I_{0}\)
3. c\(2I_{0}\)
4. d\(0\)