Wave Optics Chapter-Wise Test 21

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the refractive index of a medium if the critical angle for light passing into air is \( 39^\circ \)?

\( \sin i_c = \frac{n_2}{n_1} \), where \( n_2 = 1.0 \) (air), \( i_c = 39^\circ \).

\( \sin 39^\circ \approx 0.629 \), \( n_1 = \frac{1.0}{0.629} \approx 1.59 \).

1.43
1.33
1.59
1.85
3

In a double-slit experiment, if \( \lambda = 400 \, \text{nm} \), \( d = 0.4 \, \text{mm} \), and \( D = 2.0 \, \text{m} \), what is the distance of the third bright fringe from the central maximum?

Bright fringe position \( x_n = \frac{n \lambda D}{d} \). For the third bright fringe, \( n = 3 \).

\( \lambda = 4.0 \times 10^{-7} \, \text{m} \), \( d = 4.0 \times 10^{-4} \, \text{m} \), \( D = 2.0 \, \text{m} \).

\( x_3 = \frac{3 \times 4.0 \times 10^{-7} \times 2.0}{4.0 \times 10^{-4}} = 6.0 \times 10^{-3} \, \text{m} = 6.0 \, \text{mm} \).

6.0 mm
4.0 mm
8.0 mm
3.0 mm
1

What is the critical angle for light passing from a medium with refractive index 1.85 to air (refractive index 1.0)?

\( \sin i_c = \frac{n_2}{n_1} \), where \( n_1 = 1.85 \), \( n_2 = 1.0 \).

\( \sin i_c = \frac{1.0}{1.85} \approx 0.541 \), \( i_c = \sin^{-1}(0.541) \approx 32.7^\circ \).

36°
32.7°
37.3°
40.2°
2

What is the condition for the third secondary maximum in a single-slit diffraction pattern?

Secondary maxima occur at \( \theta \approx \frac{(n + \frac{1}{2})\lambda}{a} \). For the third secondary maximum, \( n = 3 \), \( \theta \approx \frac{7\lambda}{2a} \).

\( \theta = \frac{5\lambda}{2a} \)
\( \theta = \frac{3\lambda}{a} \)
\( \theta = \frac{2\lambda}{a} \)
\( \theta = \frac{7\lambda}{2a} \)
4

What is the distance of the third dark fringe from the central maximum in a double-slit experiment if \( \lambda = 600 \, \text{nm} \), \( d = 0.4 \, \text{mm} \), and \( D = 2.0 \, \text{m} \)?

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

\( \lambda = 6.0 \times 10^{-7} \, \text{m} \), \( d = 4.0 \times 10^{-4} \, \text{m} \), \( D = 2.0 \, \text{m} \).

\( x_2 = \frac{\left(2 + \frac{1}{2}\right) \times 6.0 \times 10^{-7} \times 2.0}{4.0 \times 10^{-4}} = \frac{2.5 \times 1.2 \times 10^{-6}}{4.0 \times 10^{-4}} = 7.5 \times 10^{-3} \, \text{m} = 7.5 \, \text{mm} \).

6.0 mm
9.0 mm
7.5 mm
4.5 mm
3

What is the nature of the wavefront produced by a plane wave after reflection from a concave mirror?

A plane wave reflecting off a concave mirror forms a spherical wavefront converging to the focal point.

Plane
Cylindrical
Tilted
Spherical
4

What is the path difference for the third dark fringe in a double-slit experiment?

Destructive interference occurs at \( \Delta = \left(n + \frac{1}{2}\right)\lambda \). For the third dark fringe, \( n = 2 \), \( \Delta = \left(2 + \frac{1}{2}\right)\lambda = \frac{5\lambda}{2} \).

\( 2\lambda \)
\( \frac{5\lambda}{2} \)
\( \frac{3\lambda}{2} \)
\( 3\lambda \)
2

What is the refractive index of a medium if the speed of light in it is \( 1.8 \times 10^8 \, \text{m/s} \) and in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

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

\( c = 3.0 \times 10^8 \, \text{m/s} \), \( v = 1.8 \times 10^8 \, \text{m/s} \).

\( n = \frac{3.0 \times 10^8}{1.8 \times 10^8} \approx 1.67 \).

1.5
1.33
1.67
1.8
3

What is the wavelength of light in a medium with refractive index 1.5 if its wavelength in vacuum is \( 750 \, \text{nm} \)?

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

Given \( \lambda_{\text{vacuum}} = 750 \, \text{nm} \), \( n = 1.5 \), \( \lambda_m = \frac{750}{1.5} = 500 \, \text{nm} \).

500 nm
600 nm
750 nm
375 nm
1

What is the shape of the wavefront reflected by a plane mirror when a spherical wave is incident on it?

A spherical wavefront incident on a plane mirror reflects as a spherical wavefront, diverging from the mirror’s virtual focus.

Spherical
Plane
Cylindrical
Tilted plane
1

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