Wave Optics Chapter-Wise Test 20

Correct answer Carries: 4.

Wrong Answer Carries: -1.

In a double-slit experiment, if two wavelengths \( 600 \, \text{nm} \) and \( 400 \, \text{nm} \) are used, what is the smallest distance from the central maximum where their bright fringes coincide? (\( d = 0.2 \, \text{mm} \), \( D = 1.0 \, \text{m} \))

Bright fringe position \( x_n = \frac{n \lambda D}{d} \). Fringes coincide when \( n_1 \lambda_1 = n_2 \lambda_2 \).

\( 600 n_1 = 400 n_2 \), \( n_2 = \frac{3}{2} n_1 \). Smallest integers: \( n_1 = 2 \), \( n_2 = 3 \).

\( x = \frac{2 \times 6.0 \times 10^{-7} \times 1.0}{2.0 \times 10^{-4}} = 6.0 \times 10^{-3} \, \text{m} = 6.0 \, \text{mm} \).

3.0 mm
4.0 mm
5.0 mm
6.0 mm
4

Why does the interference pattern from two slits disappear if the slits are too far apart?

Large slit separation reduces the overlap of wavefronts, disrupting the consistent path difference needed for stable interference.

Amplitude doubles
Frequency decreases
Reduced wavefront overlap
Wavelength increases
3

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

Destructive interference occurs at \( \Delta = \left(n + \frac{1}{2}\right)\lambda \). For the fifth dark fringe, \( n = 4 \), \( \Delta = \left(4 + \frac{1}{2}\right)\lambda = \frac{9\lambda}{2} \).

\( 4\lambda \)
\( \frac{9\lambda}{2} \)
\( \frac{7\lambda}{2} \)
\( 5\lambda \)
2

What is the speed of light in a medium if its refractive index is 1.2 and the speed in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

Speed in a medium \( v = \frac{c}{n} \).

Given \( n = 1.2 \), \( c = 3.0 \times 10^8 \, \text{m/s} \), \( v = \frac{3.0 \times 10^8}{1.2} = 2.5 \times 10^8 \, \text{m/s} \).

\( 2.5 \times 10^8 \, \text{m/s} \)
\( 2.0 \times 10^8 \, \text{m/s} \)
\( 3.0 \times 10^8 \, \text{m/s} \)
\( 1.5 \times 10^8 \, \text{m/s} \)
1

What is the angle of refraction when light is incident at the critical angle from a denser medium to a rarer medium?

At the critical angle, the angle of refraction is \( 90^\circ \), as the refracted ray travels along the boundary between the two media.

\( 0^\circ \)
\( 45^\circ \)
\( 90^\circ \)
\( 60^\circ \)
3

What is the shape of the refracted wavefront when a plane wave passes through a convex lens and converges to a point?

A plane wave passing through a convex lens forms a spherical wavefront converging to the focal point.

Spherical
Plane
Cylindrical
Tilted plane
1

What allows light to propagate through a vacuum without requiring a traditional medium?

Light consists of oscillating electric and magnetic fields that sustain each other, enabling propagation without a material medium, as explained by electromagnetic theory.

High amplitude
Electromagnetic nature
Constant wavelength
Polarization property
2

What does the wave theory predict about the speed of light when it bends towards the normal during refraction?

The wave theory predicts that if light bends towards the normal, its speed decreases in the second medium.

Speed increases
Speed remains the same
Speed becomes zero
Speed decreases
4

What is the intensity of light after passing through two polaroids with pass-axes at \( 45^\circ \), if the initial unpolarized intensity is \( I_0 \)?

After the first polaroid, \( I = \frac{I_0}{2} \). After the second at \( 45^\circ \), \( I = \frac{I_0}{2} \cos^2 45^\circ = \frac{I_0}{2} \times \frac{1}{2} = \frac{I_0}{4} \).

\( \frac{I_0}{2} \)
\( \frac{I_0}{4} \)
\( I_0 \)
\( 0 \)
2

What is the distance of the fourth bright fringe from the central maximum in a double-slit experiment if \( \lambda = 560 \, \text{nm} \), \( d = 0.35 \, \text{mm} \), and \( D = 1.4 \, \text{m} \)?

Bright fringe position \( x_n = \frac{n \lambda D}{d} \). For the fourth bright fringe, \( n = 4 \).

\( \lambda = 5.6 \times 10^{-7} \, \text{m} \), \( d = 3.5 \times 10^{-4} \, \text{m} \), \( D = 1.4 \, \text{m} \).

\( x_4 = \frac{4 \times 5.6 \times 10^{-7} \times 1.4}{3.5 \times 10^{-4}} = 8.96 \times 10^{-3} \, \text{m} = 8.96 \, \text{mm} \).

8.96 mm
6.72 mm
11.2 mm
4.48 mm
1

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