Wave Optics Chapter-Wise Test 15

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the direction of the electric field in a linearly polarized light wave relative to its propagation direction?

In a linearly polarized light wave, the electric field oscillates perpendicular to the direction of propagation.

Parallel
At 45°
Random
Perpendicular
4

What is the intensity of light after passing through three polaroids, with the first and third crossed and the second at \( 45^\circ \) to the first, if the initial unpolarized intensity is \( I_0 \)?

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

Third at \( 90^\circ - 45^\circ = 45^\circ \) to second, \( I = \frac{I_0}{4} \cos^2 45^\circ = \frac{I_0}{4} \times \frac{1}{2} = \frac{I_0}{8} \).

\( \frac{I_0}{4} \)
\( \frac{I_0}{8} \)
\( \frac{I_0}{2} \)
\( 0 \)
2

What is the angular position of the third minimum in a single-slit diffraction pattern if the slit width is \( 4.0 \, \mu\text{m} \) and the wavelength is \( 400 \, \text{nm} \)?

Minima occur at \( \sin \theta = \frac{n\lambda}{a} \). For the third minimum, \( n = 3 \).

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

\( \sin \theta = \frac{3 \times 4.0 \times 10^{-7}}{4.0 \times 10^{-6}} = 0.3 \), \( \theta = \sin^{-1}(0.3) \approx 17.5^\circ \).

15°
20°
17.5°
10°
3

What is the intensity at a point in a double-slit experiment where the path difference is \( 7\lambda/2 \), if the maximum intensity is \( 4I_0 \)?

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

For \( \Delta = \frac{7\lambda}{2} \), \( \phi = \frac{2\pi}{\lambda} \cdot \frac{7\lambda}{2} = 7\pi \), \( I = 4I_0 \cos^2\left(\frac{7\pi}{2}\right) = 4I_0 \times 0 = 0 \).

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

What is the intensity at a point in a double-slit experiment where the path difference is \( 5\lambda/2 \), if the maximum intensity is \( 4I_0 \)?

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

For \( \Delta = \frac{5\lambda}{2} \), \( \phi = \frac{2\pi}{\lambda} \cdot \frac{5\lambda}{2} = 5\pi \), \( I = 4I_0 \cos^2\left(\frac{5\pi}{2}\right) = 4I_0 \times 0 = 0 \).

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

What is the angular position of the third minimum in a single-slit diffraction pattern if the slit width is \( 10.0 \, \mu\text{m} \) and the wavelength is \( 600 \, \text{nm} \)?

Minima occur at \( \sin \theta = \frac{n\lambda}{a} \). For the third minimum, \( n = 3 \).

\( \lambda = 6.0 \times 10^{-7} \, \text{m} \), \( a = 1.0 \times 10^{-5} \, \text{m} \).

\( \sin \theta = \frac{3 \times 6.0 \times 10^{-7}}{1.0 \times 10^{-5}} = 0.18 \), \( \theta = \sin^{-1}(0.18) \approx 10.4^\circ \).

13.9°
10.4°
23.6°
9.2°
2

What is the resultant amplitude of two coherent waves of amplitude \( a \) with a phase difference of \( 5\pi/2 \)?

Resultant amplitude \( A = 2a \cos(\phi/2) \).

For \( \phi = \frac{5\pi}{2} \), \( A = 2a \cos\left(\frac{5\pi}{4}\right) = 2a \left(-\frac{\sqrt{2}}{2}\right) = -a\sqrt{2} \), magnitude \( a\sqrt{2} \).

\( 2a \)
\( 0 \)
\( a \)
\( a\sqrt{2} \)
4

What causes the intensity of light to remain conserved during interference despite the presence of dark fringes?

Energy is redistributed from dark to bright fringes through interference, conserving total energy as the sum of intensities balances out.

Speed increase
Frequency change
Amplitude doubling
Energy redistribution
4

What is the phase difference corresponding to a path difference of \( 5\lambda/4 \) in a double-slit experiment?

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

For \( \Delta = \frac{5\lambda}{4} \), \( \phi = \frac{2\pi}{\lambda} \cdot \frac{5\lambda}{4} = \frac{5\pi}{2} \).

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

What is the angular width of the central maximum in a single-slit diffraction pattern if the slit width is \( 5.0 \, \mu\text{m} \) and the wavelength is \( 650 \, \text{nm} \)?

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

\( \lambda = 6.5 \times 10^{-7} \, \text{m} \), \( a = 5.0 \times 10^{-6} \, \text{m} \).

\( \sin \theta = \frac{\lambda}{a} = \frac{6.5 \times 10^{-7}}{5.0 \times 10^{-6}} = 0.13 \), \( \theta = \sin^{-1}(0.13) \approx 7.5^\circ \), \( 2\theta \approx 15^\circ \).

17.2°
10°
15°
20°
3

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