Wave Optics Chapter-Wise Test 1

Correct answer Carries: 4.

Wrong Answer Carries: -1.

What determines the visibility of interference fringes when light passes through two slits?

Coherence, or a constant phase difference between the waves from the slits, is essential for a visible, stable interference pattern.

Amplitude equality
Wavelength variation
Constant phase difference
Speed uniformity
3

What fundamental principle allows the prediction of a new wavefront’s shape from a known wavefront using secondary wavelets?

Huygens’ principle states that every point on a wavefront acts as a source of secondary wavelets, whose envelope forms the new wavefront.

Superposition
Conservation of energy
Huygens’ principle
Malus’ law
3

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

Constructive interference occurs at \( \Delta = n\lambda \). For the seventh bright fringe, \( n = 7 \), so \( \Delta = 7\lambda \).

\( 6\lambda \)
\( 7\lambda \)
\( \frac{13\lambda}{2} \)
\( 5\lambda \)
2

What is the shape of the wavefront emitted by a point source at a large distance?

At a large distance from a point source, the spherical wavefront appears plane over a small region.

Plane
Spherical
Cylindrical
Elliptical
1

What prevents the formation of an interference pattern when two independent light sources are used?

Independent sources lack a fixed phase relationship (incoherence), causing rapid phase fluctuations that average out interference effects.

Different amplitudes
Lack of coherence
Unequal wavelengths
Speed variation
2

What is the refractive index of a medium if the speed of light in it is \( 2.25 \times 10^8 \, \text{m/s} \) and in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

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

\( c = 3.0 \times 10^8 \, \text{m/s} \), \( v = 2.25 \times 10^8 \, \text{m/s} \).

\( n = \frac{3.0 \times 10^8}{2.25 \times 10^8} = 1.33 \).

1.5
1.25
1.33
1.6
3

What is the frequency of light with a wavelength of \( 480 \, \text{nm} \) in air, given the speed of light in air is \( 3.0 \times 10^8 \, \text{m/s} \)?

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

\( \lambda = 4.8 \times 10^{-7} \, \text{m} \), \( c = 3.0 \times 10^8 \, \text{m/s} \).

\( \nu = \frac{3.0 \times 10^8}{4.8 \times 10^{-7}} = 6.25 \times 10^{14} \, \text{Hz} \).

\( 5.0 \times 10^{14} \, \text{Hz} \)
\( 6.25 \times 10^{14} \, \text{Hz} \)
\( 7.0 \times 10^{14} \, \text{Hz} \)
\( 4.0 \times 10^{14} \, \text{Hz} \)
2

What distinguishes the interference pattern of a double-slit experiment from the diffraction pattern of a single slit?

Interference involves superposition from two sources, producing evenly spaced fringes, while diffraction from one slit creates a broad central maximum with weaker secondary maxima.

Different frequencies
Amplitude variation
Number of sources
Wavelength change
3

What is the intensity of light transmitted through two polaroids with their pass-axes at \( 45^\circ \) to each other, if the initial intensity after the first polaroid is \( I_0 \)?

Using Malus’ law, \( I = I_0 \cos^2 \theta \).

For \( \theta = 45^\circ \), \( \cos 45^\circ = \frac{\sqrt{2}}{2} \), so \( I = I_0 \left(\frac{\sqrt{2}}{2}\right)^2 = I_0 \times \frac{1}{2} = \frac{I_0}{2} \).

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

Why does total internal reflection occur only when light travels from a denser to a rarer medium?

In a denser medium, the critical angle exists due to a lower speed, beyond which refraction cannot occur, leading to reflection; this doesn’t happen in the reverse direction.

Light’s amplitude increases
Wavelength doubles
Critical angle exists in denser medium
Frequency changes
3

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

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

Halves
Remains the same
Triples
Doubles
4

What is the distance of the fifth dark fringe from the central maximum in a double-slit experiment if \( \lambda = 650 \, \text{nm} \), \( d = 0.5 \, \text{mm} \), and \( D = 1.0 \, \text{m} \)?

Dark fringe position \( x_n = \frac{\left(n + \frac{1}{2}\right) \lambda D}{d} \). For the fifth dark fringe, \( n = 4 \).

\( \lambda = 6.5 \times 10^{-7} \, \text{m} \), \( d = 5.0 \times 10^{-4} \, \text{m} \), \( D = 1.0 \, \text{m} \).

\( x_4 = \frac{\left(4 + \frac{1}{2}\right) \times 6.5 \times 10^{-7} \times 1.0}{5.0 \times 10^{-4}} = \frac{4.5 \times 6.5 \times 10^{-7}}{5.0 \times 10^{-4}} = 5.85 \times 10^{-3} \, \text{m} = 5.85 \, \text{mm} \).

5.2 mm
6.5 mm
5.85 mm
7.8 mm
3

What is the nature of the interference pattern formed by incoherent sources?

Incoherent sources produce no stable interference pattern; intensities simply add up, resulting in uniform illumination.

Bright and dark fringes
Only bright fringes
Only dark fringes
Uniform illumination
4

In a single-slit diffraction pattern, what happens to the central maximum’s width if the slit width is tripled?

Angular width \( 2\theta = \frac{2\lambda}{a} \). If \( a \) is tripled, \( 2\theta \) is reduced to one-third.

Triples
Doubles
Remains the same
Reduces to one-third
4

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

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

For \( \phi = \pi/2 \), \( A = 2a \cos(\pi/4) = 2a \times \frac{\sqrt{2}}{2} = a\sqrt{2} \).

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

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