Wave Optics Chapter-Wise Test 3

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What is the wavelength of light in a medium with refractive index 1.2 if its wavelength in vacuum is \( 600 \, \text{nm} \)?

Wavelength in a medium \( \lambda_m = \frac{\lambda_{\text{vacuum}}}{n} \).

Given \( \lambda_{\text{vacuum}} = 600 \, \text{nm} \), \( n = 1.2 \), \( \lambda_m = \frac{600}{1.2} = 500 \, \text{nm} \).

500 nm
600 nm
400 nm
720 nm
1

What is the phase difference corresponding to a path difference of \( 5\lambda/8 \) in a double-slit experiment?

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

For \( \Delta = \frac{5\lambda}{8} \), \( \phi = \frac{2\pi}{\lambda} \cdot \frac{5\lambda}{8} = \frac{5\pi}{4} \).

\( \pi \)
\( \frac{3\pi}{2} \)
\( \frac{5\pi}{4} \)
\( 2\pi \)
3

What is the frequency of light with a wavelength of \( 540 \, \text{nm} \) in air, given the speed of light in air is \( 3.0 \times 10^8 \, \text{m/s} \)?

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

\( \lambda = 5.4 \times 10^{-7} \, \text{m} \), \( c = 3.0 \times 10^8 \, \text{m/s} \).

\( \nu = \frac{3.0 \times 10^8}{5.4 \times 10^{-7}} \approx 5.56 \times 10^{14} \, \text{Hz} \).

\( 5.0 \times 10^{14} \, \text{Hz} \)
\( 5.56 \times 10^{14} \, \text{Hz} \)
\( 6.0 \times 10^{14} \, \text{Hz} \)
\( 4.5 \times 10^{14} \, \text{Hz} \)
2

What happens to the wavelength of light when it enters a denser medium?

In a denser medium, the speed decreases, and since frequency remains constant, wavelength decreases (\( \lambda = \frac{v}{\nu} \)).

Increases
Remains the same
Becomes zero
Decreases
4

What is the direction of rays relative to the wavefront in a light wave?

Rays are perpendicular to the wavefront, representing the direction of energy propagation.

Parallel
At 45°
Random
Perpendicular
4

What is the path difference for the second dark fringe in a double-slit experiment?

Destructive interference occurs at \( \Delta = \left(n + \frac{1}{2}\right)\lambda \). For the second dark fringe, \( n = 1 \), \( \Delta = \left(1 + \frac{1}{2}\right)\lambda = \frac{3\lambda}{2} \).

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

What is the wavelength of light in a medium with refractive index 1.75 if its wavelength in vacuum is \( 700 \, \text{nm} \)?

Wavelength in a medium \( \lambda_m = \frac{\lambda_{\text{vacuum}}}{n} \).

Given \( \lambda_{\text{vacuum}} = 700 \, \text{nm} \), \( n = 1.75 \), \( \lambda_m = \frac{700}{1.75} = 400 \, \text{nm} \).

400 nm
700 nm
350 nm
525 nm
1

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

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

For \( \phi = \frac{\pi}{2} \), \( I = 4I_0 \cos^2\left(\frac{\pi}{4}\right) = 4I_0 \left(\frac{\sqrt{2}}{2}\right)^2 = 4I_0 \times \frac{1}{2} = 2I_0 \).

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

What is the phase difference between two coherent waves resulting in destructive interference?

Destructive interference occurs when the phase difference is an odd multiple of \( \pi \), with the simplest case being \( \phi = \pi \).

\( 0 \)
\( \pi/2 \)
\( \pi \)
\( 2\pi \)
3

Why does the wave model predict that light bends away from the normal when entering a rarer medium?

In a rarer medium, light speeds up, causing the wavefront to tilt away from the normal as it takes less time to travel a longer path.

Amplitude increases
Frequency decreases
Wavelength remains constant
Speed increases
4

What is the intensity of two incoherent light sources each of intensity \( I_0 \) when combined at a point?

For incoherent sources, intensities add directly, so \( I = I_0 + I_0 = 2I_0 \).

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

Why does the intensity of light not depend on its speed when it enters a denser medium?

Intensity depends on the amplitude squared, not speed, which only affects wavelength and not the energy carried per unit area.

Frequency increases
Wavelength remains constant
Amplitude determines intensity
Speed equals frequency
3

What is the angular position of the second minimum in a single-slit diffraction pattern if the slit width is \( 3.0 \, \mu\text{m} \) and the wavelength is \( 600 \, \text{nm} \)?

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

\( \lambda = 6.0 \times 10^{-7} \, \text{m} \), \( a = 3.0 \times 10^{-6} \, \text{m} \).

\( \sin \theta = \frac{2 \times 6.0 \times 10^{-7}}{3.0 \times 10^{-6}} = 0.4 \), \( \theta = \sin^{-1}(0.4) \approx 23.6^\circ \).

20°
23.6°
30°
15°
2

What is the phase difference corresponding to a path difference of \( 9\lambda/4 \) in a double-slit experiment?

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

For \( \Delta = \frac{9\lambda}{4} \), \( \phi = \frac{2\pi}{\lambda} \cdot \frac{9\lambda}{4} = \frac{9\pi}{2} \).

\( 5\pi \)
\( 4\pi \)
\( \frac{9\pi}{2} \)
\( \frac{7\pi}{2} \)
3

Why does light exhibit both interference and diffraction despite traveling in straight lines in everyday observations?

Light’s wavelength is very small compared to typical objects, making straight-line behavior dominant, but wave effects like interference and diffraction emerge with small apertures.

Small wavelength relative to obstacles
High frequency
Constant speed
Large amplitude
1

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