Wave Optics Chapter-Wise Test 11

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the speed of light in a medium with refractive index 1.45, given the speed in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

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

Given \( n = 1.45 \), \( c = 3.0 \times 10^8 \, \text{m/s} \), \( v = \frac{3.0 \times 10^8}{1.45} \approx 2.07 \times 10^8 \, \text{m/s} \).

\( 2.07 \times 10^8 \, \text{m/s} \)
\( 2.14 \times 10^8 \, \text{m/s} \)
\( 1.5 \times 10^8 \, \text{m/s} \)
\( 3.0 \times 10^8 \, \text{m/s} \)
1

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

The central maximum occurs at \( \theta = 0^\circ \), where the path difference is zero and intensity is maximum.

\( \theta = \frac{\lambda}{a} \)
\( \theta = \frac{3\lambda}{2a} \)
\( \theta = \frac{2\lambda}{a} \)
\( \theta = 0^\circ \)
4

What explains the presence of alternate bright and dark bands near the edge of a shadow in diffraction?

Diffraction causes light to bend around edges, with secondary wavelets interfering constructively and destructively, forming bright and dark bands.

Amplitude variation
Frequency change
Speed increase
Interference of bent light
4

What causes the secondary maxima in a single-slit diffraction pattern to be weaker than the central maximum?

Secondary maxima result from partial constructive interference of secondary wavelets, with more cancellations than the fully in-phase central maximum, reducing intensity.

Increased frequency
Partial interference of wavelets
Amplitude reduction
Wavelength variation
2

What is the fringe width in a double-slit experiment if \( \lambda = 620 \, \text{nm} \), \( d = 0.5 \, \text{mm} \), and \( D = 2.0 \, \text{m} \)?

Fringe width \( \beta = \frac{\lambda D}{d} \).

\( \lambda = 6.2 \times 10^{-7} \, \text{m} \), \( d = 5.0 \times 10^{-4} \, \text{m} \), \( D = 2.0 \, \text{m} \).

\( \beta = \frac{6.2 \times 10^{-7} \times 2.0}{5.0 \times 10^{-4}} = 2.48 \times 10^{-3} \, \text{m} = 2.48 \, \text{mm} \).

2.48 mm
1.24 mm
3.72 mm
4.96 mm
1

In a diffraction experiment, if the slit width is \( 4.0 \, \mu\text{m} \) and the wavelength is \( 800 \, \text{nm} \), what is the angular position of the first minimum?

First minimum occurs at \( \sin \theta = \frac{\lambda}{a} \).

\( \lambda = 800 \, \text{nm} = 8.0 \times 10^{-7} \, \text{m} \), \( a = 4.0 \, \mu\text{m} = 4.0 \times 10^{-6} \, \text{m} \).

\( \sin \theta = \frac{8.0 \times 10^{-7}}{4.0 \times 10^{-6}} = 0.2 \), so \( \theta = \sin^{-1}(0.2) \approx 11.5^\circ \).

\( 10^\circ \)
\( 15^\circ \)
\( 11.5^\circ \)
\( 20^\circ \)
3

What is the angular width of the central maximum in a single-slit diffraction pattern if the slit width is \( 12.0 \, \mu\text{m} \) and the wavelength is \( 480 \, \text{nm} \)?

Angular width \( 2\theta = \frac{2\lambda}{a} \).

\( \lambda = 4.8 \times 10^{-7} \, \text{m} \), \( a = 1.2 \times 10^{-5} \, \text{m} \).

\( \sin \theta = \frac{\lambda}{a} = \frac{4.8 \times 10^{-7}}{1.2 \times 10^{-5}} = 0.04 \), \( \theta = \sin^{-1}(0.04) \approx 2.3^\circ \), \( 2\theta \approx 4.6^\circ \).

9.2°
2.9°
4.6°
13.9°
3

What is the distance of the third dark fringe from the central maximum in a double-slit experiment if \( \lambda = 550 \, \text{nm} \), \( d = 0.25 \, \text{mm} \), 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, \( n = 2 \).

\( \lambda = 5.5 \times 10^{-7} \, \text{m} \), \( d = 2.5 \times 10^{-4} \, \text{m} \), \( D = 2.0 \, \text{m} \).

\( x_2 = \frac{\left(2 + \frac{1}{2}\right) \times 5.5 \times 10^{-7} \times 2.0}{2.5 \times 10^{-4}} = \frac{2.5 \times 1.1 \times 10^{-6}}{2.5 \times 10^{-4}} = 1.1 \times 10^{-2} \, \text{m} = 11 \, \text{mm} \).

8.8 mm
13.2 mm
11 mm
6.6 mm
3

Why can’t two ordinary light sources, like sodium lamps, produce a stable interference pattern when illuminating two slits?

Ordinary sources emit light with rapidly changing phase differences, making them incoherent and unable to maintain a stable interference pattern.

They emit different wavelengths
They are incoherent due to random phase changes
Their amplitudes are unequal
They produce longitudinal waves
2

What is the speed of light in a medium with a refractive index of 1.5, given the speed of light in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

Refractive index \( n = \frac{c}{v} \), where \( c \) is the speed in vacuum and \( v \) is the speed in the medium.

Given \( n = 1.5 \), \( v = \frac{c}{n} = \frac{3.0 \times 10^8}{1.5} = 2.0 \times 10^8 \, \text{m/s} \).

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

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