Wave Optics Chapter-Wise Test 19

Correct answer Carries: 4.

Wrong Answer Carries: -1.

In a diffraction pattern, what happens to the angular width of the central maximum if the slit width is doubled?

Angular width of the central maximum is \( 2\theta = \frac{2\lambda}{a} \). If \( a \) is doubled, \( 2\theta \) is halved.

Doubles
Quadruples
Remains the same
Halves
4

What is the frequency of light with a wavelength of \( 510 \, \text{nm} \) in air, given the speed of light in air is \( 3.0 \times 10^8 \, \text{m/s} \)?

Frequency \( \nu = \frac{c}{\lambda} \).

\( \lambda = 5.1 \times 10^{-7} \, \text{m} \), \( c = 3.0 \times 10^8 \, \text{m/s} \).

\( \nu = \frac{3.0 \times 10^8}{5.1 \times 10^{-7}} \approx 5.88 \times 10^{14} \, \text{Hz} \).

\( 5.0 \times 10^{14} \, \text{Hz} \)
\( 5.88 \times 10^{14} \, \text{Hz} \)
\( 6.25 \times 10^{14} \, \text{Hz} \)
\( 4.5 \times 10^{14} \, \text{Hz} \)
2

What is the intensity at a point in a double-slit experiment where the phase difference is \( 3\pi \), if the maximum intensity is \( 4I_0 \)?

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

For \( \phi = 3\pi \), \( I = 4I_0 \cos^2\left(\frac{3\pi}{2}\right) = 4I_0 \times 0 = 0 \).

\( 2I_0 \)
\( I_0 \)
\( 0 \)
\( 4I_0 \)
3

What is the condition for the fifth minimum in a single-slit diffraction pattern?

Minima occur at \( \sin \theta = \frac{n\lambda}{a} \). For the fifth minimum, \( n = 5 \), so \( \theta = \sin^{-1}\left(\frac{5\lambda}{a}\right) \).

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

What is the shape of the wavefront after a plane wave passes through a thin prism?

A plane wave passing through a prism gets tilted due to the varying thickness, resulting in a tilted plane wavefront.

Spherical
Tilted plane
Cylindrical
Curved
2

What is the speed of light in a medium with refractive index 1.25, given the speed in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

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

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

\( 2.4 \times 10^8 \, \text{m/s} \)
\( 2.0 \times 10^8 \, \text{m/s} \)
\( 3.0 \times 10^8 \, \text{m/s} \)
\( 1.5 \times 10^8 \, \text{m/s} \)
1

What is the frequency of light with a wavelength of \( 600 \, \text{nm} \) in air, given the speed of light in air is \( 3.0 \times 10^8 \, \text{m/s} \)?

Frequency \( \nu = \frac{c}{\lambda} \).

\( \lambda = 600 \, \text{nm} = 6.0 \times 10^{-7} \, \text{m} \), \( c = 3.0 \times 10^8 \, \text{m/s} \).

\( \nu = \frac{3.0 \times 10^8}{6.0 \times 10^{-7}} = 5.0 \times 10^{14} \, \text{Hz} \).

\( 4.0 \times 10^{14} \, \text{Hz} \)
\( 5.0 \times 10^{14} \, \text{Hz} \)
\( 6.0 \times 10^{14} \, \text{Hz} \)
\( 7.0 \times 10^{14} \, \text{Hz} \)
2

What is the angular position of the first minimum in a single-slit diffraction pattern if the slit width is \( 8.0 \, \mu\text{m} \) and the wavelength is \( 640 \, \text{nm} \)?

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

\( \lambda = 6.4 \times 10^{-7} \, \text{m} \), \( a = 8.0 \times 10^{-6} \, \text{m} \).

\( \sin \theta = \frac{6.4 \times 10^{-7}}{8.0 \times 10^{-6}} = 0.08 \), \( \theta = \sin^{-1}(0.08) \approx 4.6^\circ \).

5.7°
3.0°
4.6°
8.6°
3

What is the distance of the fifth bright fringe from the central maximum in a double-slit experiment if \( \lambda = 490 \, \text{nm} \), \( d = 0.5 \, \text{mm} \), and \( D = 1.0 \, \text{m} \)?

Bright fringe position \( x_n = \frac{n \lambda D}{d} \). For the fifth bright fringe, \( n = 5 \).

\( \lambda = 4.9 \times 10^{-7} \, \text{m} \), \( d = 5.0 \times 10^{-4} \, \text{m} \), \( D = 1.0 \, \text{m} \).

\( x_5 = \frac{5 \times 4.9 \times 10^{-7} \times 1.0}{5.0 \times 10^{-4}} = 4.9 \times 10^{-3} \, \text{m} = 4.9 \, \text{mm} \).

4.9 mm
3.9 mm
5.9 mm
2.45 mm
1

What causes the intensity of light to be zero at certain points in a diffraction pattern?

Complete destructive interference occurs when secondary wavelets from different parts of the slit cancel each other out, resulting in zero intensity at minima.

Amplitude increase
Frequency shift
Destructive interference
Speed variation
3

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