Wave Optics Chapter-Wise Test 2

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What happens to the frequency of light when it refracts from air into water?

The frequency of light depends on the source and remains constant during refraction, as only speed and wavelength change with the medium.

Remains the same
Increases
Decreases
Doubles
1

What is the angular position of the fourth minimum in a single-slit diffraction pattern if the slit width is \( 5.0 \, \mu\text{m} \) and the wavelength is \( 500 \, \text{nm} \)?

Minima occur at \( \sin \theta = \frac{n\lambda}{a} \). For the fourth minimum, \( n = 4 \).

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

\( \sin \theta = \frac{4 \times 5.0 \times 10^{-7}}{5.0 \times 10^{-6}} = 0.4 \), \( \theta = \sin^{-1}(0.4) \approx 23.6^\circ \).

17.5°
20°
23.6°
13.9°
3

When a plane wave reflects off a plane surface, what is the relationship between the angle of incidence and the angle of reflection?

The law of reflection states that the angle of incidence equals the angle of reflection.

Angle of incidence = Angle of reflection
Angle of incidence > Angle of reflection
Angle of incidence < Angle of reflection
Angle of reflection = 90°
1

Why does the intensity of light transmitted through three polaroids reach a maximum when the middle one is at 45° to the crossed first and third polaroids?

At 45°, the middle polaroid allows maximum projection of the polarized light from the first to pass through the third, optimizing the cosine-squared term in Malus’ law.

Frequency alignment
Wavelength matching
Amplitude doubling
Maximum projection of polarization
4

What is the intensity of light after passing through two polaroids with pass-axes at \( 60^\circ \), if the initial unpolarized intensity is \( I_0 \)?

After the first polaroid, \( I = \frac{I_0}{2} \). After the second at \( 60^\circ \), \( I = \frac{I_0}{2} \cos^2 60^\circ = \frac{I_0}{2} \times \frac{1}{4} = \frac{I_0}{8} \).

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

What is the intensity of light after passing through two polaroids with their pass-axes perpendicular to each other, if the initial intensity is \( I_0 \)?

After the first polaroid, intensity is \( \frac{I_0}{2} \). For the second polaroid at \( 90^\circ \), \( I = \frac{I_0}{2} \cos^2 90^\circ = \frac{I_0}{2} \times 0 = 0 \).

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

What property of light waves causes the bending of rays around corners in a diffraction experiment?

Light’s wave nature allows it to spread and bend around obstacles when encountering apertures comparable to its wavelength, unlike particle-like straight paths.

Wave nature
High speed
Constant frequency
Polarization
1

What ensures that a convex lens can focus light from a plane wave into a single point?

The lens delays the central part of the plane wave more than the edges due to its thickness, transforming it into a spherical wavefront converging at the focus.

Differential delay across the lens
Increase in light speed
Uniform amplitude
Change in frequency
1

What is the shape of the wavefront after a plane wave reflects off a plane mirror?

A plane wave reflecting off a plane mirror remains a plane wavefront, as the reflection preserves its flat nature.

Spherical
Cylindrical
Tilted
Plane
4

What is the speed of light in a medium with refractive index 1.3, given the speed in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

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

Given \( n = 1.3 \), \( c = 3.0 \times 10^8 \, \text{m/s} \), \( v = \frac{3.0 \times 10^8}{1.3} \approx 2.31 \times 10^8 \, \text{m/s} \).

\( 2.31 \times 10^8 \, \text{m/s} \)
\( 2.07 \times 10^8 \, \text{m/s} \)
\( 1.5 \times 10^8 \, \text{m/s} \)
\( 3.0 \times 10^8 \, \text{m/s} \)
1

In a single-slit diffraction pattern, what happens to the intensity of secondary maxima as their order increases?

The intensity of secondary maxima decreases with increasing order, becoming weaker away from the central maximum.

Increases
Remains the same
Becomes zero
Decreases
4

What is the effect on the energy of a light wave when its speed decreases in a denser medium?

Energy of a light wave depends on its amplitude, not its speed, so it remains unchanged when speed decreases.

Remains unchanged
Decreases
Increases
Becomes zero
1

What is the frequency of light with a wavelength of \( 630 \, \text{nm} \) in air, given the speed of light in air is \( 3.0 \times 10^8 \, \text{m/s} \)?

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

\( \lambda = 6.3 \times 10^{-7} \, \text{m} \), \( c = 3.0 \times 10^8 \, \text{m/s} \).

\( \nu = \frac{3.0 \times 10^8}{6.3 \times 10^{-7}} \approx 4.76 \times 10^{14} \, \text{Hz} \).

\( 5.56 \times 10^{14} \, \text{Hz} \)
\( 4.76 \times 10^{14} \, \text{Hz} \)
\( 5.0 \times 10^{14} \, \text{Hz} \)
\( 6.25 \times 10^{14} \, \text{Hz} \)
2

What is the distance of the sixth bright fringe from the central maximum in a double-slit experiment if \( \lambda = 470 \, \text{nm} \), \( d = 0.4 \, \text{mm} \), and \( D = 2.0 \, \text{m} \)?

Bright fringe position \( x_n = \frac{n \lambda D}{d} \). For the sixth bright fringe, \( n = 6 \).

\( \lambda = 4.7 \times 10^{-7} \, \text{m} \), \( d = 4.0 \times 10^{-4} \, \text{m} \), \( D = 2.0 \, \text{m} \).

\( x_6 = \frac{6 \times 4.7 \times 10^{-7} \times 2.0}{4.0 \times 10^{-4}} = 1.41 \times 10^{-2} \, \text{m} = 14.1 \, \text{mm} \).

14.1 mm
11.75 mm
9.4 mm
16.45 mm
1

What is the speed of light in a medium with refractive index 1.6, given the speed in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

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

Given \( n = 1.6 \), \( c = 3.0 \times 10^8 \, \text{m/s} \), \( v = \frac{3.0 \times 10^8}{1.6} = 1.875 \times 10^8 \, \text{m/s} \).

\( 1.875 \times 10^8 \, \text{m/s} \)
\( 2.31 \times 10^8 \, \text{m/s} \)
\( 1.5 \times 10^8 \, \text{m/s} \)
\( 2.07 \times 10^8 \, \text{m/s} \)
1

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