Wave Optics Chapter-Wise Test 9

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the wavelength of light in a medium with refractive index 1.6 if its wavelength in vacuum is \( 640 \, \text{nm} \)?

Wavelength in a medium \( \lambda_m = \frac{\lambda_{\text{vacuum}}}{n} \).

Given \( \lambda_{\text{vacuum}} = 640 \, \text{nm} \), \( n = 1.6 \), \( \lambda_m = \frac{640}{1.6} = 400 \, \text{nm} \).

400 nm
640 nm
320 nm
500 nm
1

What is the intensity at a point in a double-slit experiment where the phase difference is \( \pi/4 \), if the maximum intensity is \( 4I_0 \)?

Intensity \( I = 4I_0 \cos^2(\phi/2) \).

For \( \phi = \frac{\pi}{4} \), \( I = 4I_0 \cos^2\left(\frac{\pi}{8}\right) \), \( \cos \frac{\pi}{8} \approx 0.923 \), \( I = 4I_0 \times (0.923)^2 \approx 4I_0 \times 0.853 \approx 3.41 I_0 \).

Closest option: \( 3I_0 \) (simplified for NEET).

\( I_0 \)
\( 2I_0 \)
\( 3I_0 \)
\( 4I_0 \)
3

What is the resultant amplitude of two coherent waves of amplitude \( a \) with a phase difference of \( 5\pi \)?

Resultant amplitude \( A = 2a \cos(\phi/2) \).

For \( \phi = 5\pi \), \( A = 2a \cos\left(\frac{5\pi}{2}\right) = 2a \times 0 = 0 \).

\( a\sqrt{2} \)
\( 2a \)
\( a \)
\( 0 \)
4

What type of wavefront emerges from a convex lens when a plane wave is incident on it?

A plane wave incident on a convex lens produces a spherical wavefront converging to the focal point.

Spherical
Plane
Cylindrical
Tilted plane
1

Why does the interference pattern disappear if the phase difference between two sources changes rapidly over time?

Rapid phase changes make the sources incoherent, averaging out the interference effects, resulting in a uniform intensity distribution.

Amplitude becomes zero
Sources become incoherent
Wavelength increases
Frequency decreases
2

What type of wave is light, based on the direction of its electric field relative to its propagation direction?

Light is a transverse wave because its electric field oscillates perpendicular to the direction of propagation.

Transverse
Longitudinal
Stationary
Mechanical
1

What is the wavelength of light in a medium with refractive index 1.5 if its wavelength in air is \( 720 \, \text{nm} \)?

Wavelength in a medium \( \lambda_m = \frac{\lambda_{\text{air}}}{n} \).

Given \( \lambda_{\text{air}} = 720 \, \text{nm} \), \( n = 1.5 \), \( \lambda_m = \frac{720}{1.5} = 480 \, \text{nm} \).

480 nm
720 nm
360 nm
600 nm
1

What is the refractive index of a medium if the speed of light in it is \( 2.4 \times 10^8 \, \text{m/s} \) and in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

Refractive index \( n = \frac{c}{v} \).

\( c = 3.0 \times 10^8 \, \text{m/s} \), \( v = 2.4 \times 10^8 \, \text{m/s} \), \( n = \frac{3.0 \times 10^8}{2.4 \times 10^8} = 1.25 \).

1.5
1.25
1.33
2.0
2

What is the distance of the fourth dark fringe from the central maximum in a double-slit experiment if \( \lambda = 610 \, \text{nm} \), \( d = 0.3 \, \text{mm} \), and \( D = 1.5 \, \text{m} \)?

Dark fringe position \( x_n = \frac{\left(n + \frac{1}{2}\right) \lambda D}{d} \). For the fourth dark fringe, \( n = 3 \).

\( \lambda = 6.1 \times 10^{-7} \, \text{m} \), \( d = 3.0 \times 10^{-4} \, \text{m} \), \( D = 1.5 \, \text{m} \).

\( x_3 = \frac{\left(3 + \frac{1}{2}\right) \times 6.1 \times 10^{-7} \times 1.5}{3.0 \times 10^{-4}} = \frac{3.5 \times 9.15 \times 10^{-7}}{3.0 \times 10^{-4}} = 1.0675 \times 10^{-2} \, \text{m} \approx 10.7 \, \text{mm} \).

9.15 mm
12.2 mm
10.7 mm
7.6 mm
3

What is the refractive index of a medium if the critical angle for light passing into air is \( 42^\circ \)?

\( \sin i_c = \frac{n_2}{n_1} \), where \( n_2 = 1.0 \) (air), \( i_c = 42^\circ \).

\( \sin 42^\circ \approx 0.669 \), \( n_1 = \frac{1.0}{0.669} \approx 1.49 \).

1.33
1.67
1.49
1.55
3

Performance Summary

Score:

Category Details
Total Attempts:
Total Skipped:
Total Wrong Answers:
Total Correct Answers:
Time Taken:
Average Time Taken per Question:
Accuracy:
0