Wave Optics Chapter-Wise Test 6

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the path difference for the third bright fringe in a double-slit experiment?

Constructive interference occurs at \( \Delta = n\lambda \). For the third bright fringe, \( n = 3 \), so \( \Delta = 3\lambda \).

\( 2\lambda \)
\( 3\lambda \)
\( \lambda \)
\( \frac{3\lambda}{2} \)
2

What is the nature of light waves demonstrated by polarization?

Polarization shows that light waves are transverse, as only transverse waves can be polarized.

Transverse
Longitudinal
Stationary
Mechanical
1

What ensures that the laws of reflection hold true when derived using the wave model?

The wave model uses secondary wavelets, where the reflected wavefront’s envelope forms when the incident and reflected angles are equal, satisfying geometric congruence.

Frequency matching
Amplitude variation
Wavelength adjustment
Equal angles of incidence and reflection
4

What is the phase difference corresponding to a path difference of \( 7\lambda/4 \) in a double-slit experiment?

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

For \( \Delta = \frac{7\lambda}{4} \), \( \phi = \frac{2\pi}{\lambda} \cdot \frac{7\lambda}{4} = \frac{7\pi}{2} \).

\( 3\pi \)
\( \pi \)
\( \frac{7\pi}{2} \)
\( 2\pi \)
3

What is the angular position of the second minimum in a single-slit diffraction pattern if the slit width is \( 2.0 \, \mu\text{m} \) and the wavelength is \( 400 \, \text{nm} \)?

Minima occur at \( \sin \theta = \frac{n\lambda}{a} \). For the second minimum, \( n = 2 \).

\( \lambda = 4.0 \times 10^{-7} \, \text{m} \), \( a = 2.0 \times 10^{-6} \, \text{m} \).

\( \sin \theta = \frac{2 \times 4.0 \times 10^{-7}}{2.0 \times 10^{-6}} = 0.4 \), \( \theta = \sin^{-1}(0.4) \approx 23.6^\circ \).

20°
23.6°
30°
15°
2

What is the refractive index of a medium if the critical angle for light passing into air is \( 48.6^\circ \)?

\( \sin i_c = \frac{n_2}{n_1} \), where \( n_2 = 1.0 \) (air), \( i_c = 48.6^\circ \).

\( \sin 48.6^\circ \approx 0.75 \), \( n_1 = \frac{1.0}{0.75} \approx 1.33 \).

1.5
1.25
1.33
1.6
3

What is the speed of light in a medium with refractive index 1.35, given the speed in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

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

Given \( n = 1.35 \), \( c = 3.0 \times 10^8 \, \text{m/s} \), \( v = \frac{3.0 \times 10^8}{1.35} \approx 2.22 \times 10^8 \, \text{m/s} \).

\( 2.22 \times 10^8 \, \text{m/s} \)
\( 2.0 \times 10^8 \, \text{m/s} \)
\( 1.5 \times 10^8 \, \text{m/s} \)
\( 3.0 \times 10^8 \, \text{m/s} \)
1

What happens to the refracted wavefront when light enters a medium where its speed increases?

When speed increases (e.g., from glass to air), the refracted wavefront bends away from the normal.

Bends towards the normal
Bends away from the normal
Remains unchanged
Becomes spherical
2

Why does the wave theory predict that light bends towards the normal when entering a medium where its speed is lower?

The wavefront tilts towards the normal because the part entering the slower medium lags, reducing the angle of propagation relative to the boundary.

Amplitude decreases
Frequency increases
Wavelength doubles
Wavefront tilts due to slower speed
4

What is the refractive index of a medium if the speed of light in it is \( 2.1 \times 10^8 \, \text{m/s} \) and in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

Refractive index \( n = \frac{c}{v} \).

\( c = 3.0 \times 10^8 \, \text{m/s} \), \( v = 2.1 \times 10^8 \, \text{m/s} \).

\( n = \frac{3.0 \times 10^8}{2.1 \times 10^8} \approx 1.43 \).

1.5
1.33
1.43
1.67
3

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