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Class 12 Physics Chapter 10: Wave Optics MCQs with answers

10 multiple-choice questions on Wave Optics, each with its answer and the reason, written from the NCERT chapter. For the CBSE board, JEE Main and NEET, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
In Huygens' construction, the position of a wavefront at a later time is found as
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Answer: (d) the forward envelope (common tangent) of the secondary wavelets from every point of the earlier wavefront

Each point of the wavefront is a source of secondary wavelets spreading with the wave's speed; their common tangent (envelope) after time τ is the new wavefront. The centres of the wavelets lie on the old wavefront, not the new one.

Question 2
In a wave, the energy travels
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Answer: (a) perpendicular to the wavefront

A wavefront is a surface of constant phase, and the energy of the wave travels perpendicular to it, for spherical and plane waves alike; that direction is the ray.

Question 3
A plane wavefront falls on a thin convex lens. The wavefront that emerges is
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Answer: (c) spherical, converging to the focus, because the central part travels through the greatest thickness of glass and is delayed most

The central part of the wavefront passes through the thickest glass, where light is slower, so it lags behind the edges; the wavefront becomes spherical and converges to the focus. A tilted plane wavefront is what a thin prism gives.

Question 4
Light of frequency 6.0 × 10¹⁴ Hz has a wavelength of 400 nm inside a transparent plastic. Taking c = 3.0 × 10⁸ m s⁻¹, the refractive index of the plastic is
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Answer: (c) 1.25

The frequency is the same in every medium, so the speed in the plastic is v = νλ = 6.0 × 10¹⁴ × 400 × 10⁻⁹ = 2.4 × 10⁸ m s⁻¹, and n = c/v = 3.0/2.4 = 1.25. 0.80 is v/c, inverted; 1.33 is the index of water, assumed rather than worked out; 2.40 is the speed in units of 10⁸ m s⁻¹.

Question 5
A beam of light passes from glass into air. The quantity that does not change is its
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Answer: (a) frequency

In the Huygens construction a crest from A reaches E as the crest from B reaches C, so v₁/λ₁ = v₂/λ₂: the frequency is unchanged, while speed and wavelength both increase in air and an oblique ray bends.

Question 6
In the Huygens construction for refraction, a plane wavefront meets a plane interface at 60°. In the time the end B of the wavefront travels 6.0 cm in the first medium to reach the interface, the secondary wavelet from the other end A grows to a radius of 4.0 cm in the second medium. The angle of refraction is
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Answer: (d) 35.3°

BC = v₁τ = 6.0 cm and AE = v₂τ = 4.0 cm. From triangles ABC and AEC, sin i = BC/AC and sin r = AE/AC, so sin r = sin 60° × 4.0/6.0 = 0.866 × 0.667 = 0.577 and r ≈ 35.3°. 40.0° scales the angle instead of its sine; 54.7° is the complement of r; 60.0° ignores the change in speed.

Question 7
When light bends towards the normal on entering water, the wave theory predicts that its speed in water is
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Answer: (b) less than in air, which experiment later confirmed

With r < i, sin i/sin r = v₁/v₂ gives v₂ < v₁: light is slower in water. The corpuscular model predicted a greater speed; Foucault's measurement showed the speed in water to be less, as the wave theory said.

Question 8
Light travels at 2.0 × 10⁸ m s⁻¹ in a certain glass. Taking c = 3.0 × 10⁸ m s⁻¹, the critical angle for light going from this glass into air is
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Answer: (b) 41.8°

n = c/v = 1.5, and sin ic = n₂/n₁ = 1/1.5 = 2/3, so ic ≈ 41.8°. 48.2° is the complement; 33.7° takes tan ic = 2/3; 19.5° takes sin ic = 1/3.

Question 9
A convex lens forms a real image of a point object. The ray through the centre of the lens covers a shorter geometrical path than a ray through the edge, yet both reach the image together because
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Answer: (d) the central ray spends more of its path in glass, where light travels more slowly

The time from object point to image point is the same along every ray. The central ray's path is shorter, but more of it lies in glass, where light is slower; the two effects balance.

Question 10
According to the superposition principle, the resultant displacement at a point where several waves meet is
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Answer: (a) the vector sum of the displacements due to each wave

The resultant displacement is the vector sum of the displacements produced by each wave. Intensities add only for incoherent sources, and that is a time average, not a displacement.

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