Wave Optics Chapter-Wise Test 10

Correct answer Carries: 4.

Wrong Answer Carries: -1.

In a double-slit experiment, if the screen distance is doubled, what happens to the fringe width?

Fringe width \( \beta = \frac{\lambda D}{d} \). If \( D \) is doubled, \( \beta \) doubles.

Halves
Remains the same
Quadruples
Doubles
4

What is the phase difference corresponding to a path difference of \( 3\lambda/2 \) in a double-slit experiment?

Phase difference \( \phi = \frac{2\pi}{\lambda} \Delta \).

For \( \Delta = \frac{3\lambda}{2} \), \( \phi = \frac{2\pi}{\lambda} \cdot \frac{3\lambda}{2} = 3\pi \).

\( \pi \)
\( 2\pi \)
\( 3\pi \)
\( \pi/2 \)
3

What is the frequency of light with a wavelength of \( 570 \, \text{nm} \) in air, given the speed of light in air is \( 3.0 \times 10^8 \, \text{m/s} \)?

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

\( \lambda = 5.7 \times 10^{-7} \, \text{m} \), \( c = 3.0 \times 10^8 \, \text{m/s} \).

\( \nu = \frac{3.0 \times 10^8}{5.7 \times 10^{-7}} \approx 5.26 \times 10^{14} \, \text{Hz} \).

\( 5.88 \times 10^{14} \, \text{Hz} \)
\( 5.26 \times 10^{14} \, \text{Hz} \)
\( 4.76 \times 10^{14} \, \text{Hz} \)
\( 6.25 \times 10^{14} \, \text{Hz} \)
2

In a double-slit experiment, if the path difference at a point is \( \lambda/2 \), what is the resulting intensity if the maximum intensity is \( 4I_0 \)?

Intensity \( I = 4I_0 \cos^2(\phi/2) \), where \( \phi = \frac{2\pi}{\lambda} \Delta \).

For \( \Delta = \lambda/2 \), \( \phi = \frac{2\pi}{\lambda} \cdot \frac{\lambda}{2} = \pi \), so \( I = 4I_0 \cos^2(\pi/2) = 4I_0 \times 0 = 0 \).

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

Why does the wave theory suggest that light’s behavior approximates straight-line propagation in large-scale scenarios?

Light’s wavelength is extremely small compared to everyday objects, minimizing wave effects like diffraction, making straight-line propagation dominant.

High speed
Small wavelength
Constant phase
Large amplitude
1

What is the speed of light in a medium with refractive index 1.4, given the speed in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

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

Given \( n = 1.4 \), \( c = 3.0 \times 10^8 \, \text{m/s} \), \( v = \frac{3.0 \times 10^8}{1.4} \approx 2.14 \times 10^8 \, \text{m/s} \).

\( 2.14 \times 10^8 \, \text{m/s} \)
\( 2.0 \times 10^8 \, \text{m/s} \)
\( 1.5 \times 10^8 \, \text{m/s} \)
\( 3.0 \times 10^8 \, \text{m/s} \)
1

What happens to the fringe width in a double-slit experiment if the wavelength of light is halved?

Fringe width \( \beta = \frac{\lambda D}{d} \). If \( \lambda \) is halved, \( \beta \) is halved.

Doubles
Remains the same
Quadruples
Halves
4

What happens to the central maximum’s width in a single-slit diffraction pattern if the wavelength is doubled?

Angular width \( 2\theta = \frac{2\lambda}{a} \). If \( \lambda \) doubles, the width doubles.

Halves
Remains the same
Quadruples
Doubles
4

Why does the wave theory predict a change in wavelength but not frequency during refraction?

Frequency is source-dependent and constant, while wavelength adjusts inversely to the speed change in the medium (v = fλ), maintaining the wave equation.

Amplitude varies
Speed equals frequency
Frequency is source-dependent
Phase shifts randomly
3

What is the intensity of light after passing through two polaroids with pass-axes at \( 15^\circ \), if the initial unpolarized intensity is \( I_0 \)?

After the first polaroid, \( I = \frac{I_0}{2} \). After the second at \( 15^\circ \), \( I = \frac{I_0}{2} \cos^2 15^\circ \).

\( \cos 15^\circ \approx 0.966 \), \( I = \frac{I_0}{2} \times (0.966)^2 = \frac{I_0}{2} \times 0.933 \approx 0.467 I_0 \approx \frac{I_0}{2} \) (approx.).

Closest option adjusted for simplicity: \( \frac{7I_0}{16} \) (since \( 0.933 \approx 7/8 \)).

\( \frac{I_0}{4} \)
\( \frac{7I_0}{16} \)
\( \frac{I_0}{8} \)
\( \frac{I_0}{2} \)
2

Performance Summary

Score:

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