Chapter 10: Wave Optics Short Questions | physics Class 12 CBSE

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Chapter 10: Wave Optics Short Questions | physics Class 12 CBSE | ByteNotes.in

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Question 1

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Define a wavefront and state the relationship between the direction of energy propagation and the wavefront.

A wavefront is a surface of constant phase — it is the locus of all points in a medium that are oscillating in phase with each other at any given instant.
The speed with which the wavefront moves outward from the source is equal to the speed of the wave in that medium.
The energy of the wave always travels in a direction perpendicular to the wavefront; this perpendicular direction defines the ray direction.

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Question 2

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State Huygens principle and explain how it accounts for the forward propagation of a wavefront while ruling out the backwave.

Huygens principle states that every point on a wavefront is the source of secondary disturbances (secondary wavelets) that spread out in all directions with the speed of the wave, and the common tangent (envelope) to these wavelets gives the new wavefront at a later time.
Huygens argued, as an ad hoc assumption, that the amplitude of secondary wavelets is maximum in the forward direction and zero in the backward direction, thus explaining the absence of a backwave.
This ad hoc assumption is not fully satisfactory; the absence of the backwave is rigorously justified only by the more advanced wave theory.

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Question 3

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Using Huygens principle, explain why a plane wave incident on a convex lens produces a converging spherical wavefront on the other side.

When a plane wave hits a convex lens, the central portion of the wavefront traverses the thickest part of the lens where the speed of light is reduced (since glass is denser than air), causing the greatest delay at the centre.
The edges of the wavefront travel through thinner glass and are delayed less, so the emerging wavefront has a depression at the centre and curves inward.
This curved emerging wavefront is spherical and converges toward the focal point F of the lens, consistent with the lens focusing parallel rays to a point.

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Question 4

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What is the critical angle? Write the expression for the critical angle in terms of refractive indices and state the condition for total internal reflection.

The critical angle ic is defined as the angle of incidence in the denser medium at which the angle of refraction in the rarer medium becomes exactly 90°, given by sin ic = n2/n1.
For angles of incidence greater than ic, no refracted wave exists and the incident wave undergoes total internal reflection — all light is reflected back into the denser medium.
Total internal reflection requires two conditions: light must travel from a denser to a rarer medium, and the angle of incidence must exceed the critical angle.

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Question 5

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Derive Snell's law of refraction using Huygens principle for a plane wave incident on an interface between two media.

Consider a plane wavefront AB incident at angle i. In time τ, point B travels distance BC = v1τ in medium 1 while point A refracts into medium 2; a sphere of radius v2τ is drawn from A, and the tangent CE gives the refracted wavefront.
From triangles ABC and AEC: sin i = BC/AC = v1τ/AC and sin r = AE/AC = v2τ/AC, so sin i/sin r = v1/v2.
Since refractive index n = c/v, we get n1 sin i = n2 sin r, which is Snell's law of refraction.

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Question 6

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When a light wave is refracted into a denser medium, which of the following change: speed, wavelength, frequency? Justify your answer.

Both the speed and the wavelength of light decrease when it enters a denser medium, because v2 < v1 implies λ2 < λ1 (since v/λ = constant frequency).
The frequency does not change; frequency ν = v/λ remains the same in both media because the wave equation v1/λ1 = v2/λ2 holds at the interface.
This is consistent with the boundary condition that the wave crests must arrive and leave the interface at the same rate, keeping frequency invariant across any interface.

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Question 7

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State the superposition principle as applied to light waves and explain its role in the formation of an interference pattern.

The superposition principle states that at any point in the medium, the resultant displacement produced by multiple waves is the vector sum of the individual displacements caused by each wave independently.
When two coherent light waves overlap, the superposition produces an interference term in addition to the sum of individual intensities; this term is non-zero only when the sources have the same frequency and a stable phase difference.
The interference term gives rise to spatial variation of intensity — maxima (bright fringes) where waves add constructively and minima (dark fringes) where they cancel destructively — forming a stable, observable fringe pattern.

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Question 8

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Write the conditions for constructive and destructive interference in terms of path difference for two coherent sources vibrating in phase.

Constructive interference (maximum intensity = 4I0) occurs when the path difference S1P ~ S2P = nλ, where n = 0, 1, 2, 3, …; at these points the waves arrive in phase.
Destructive interference (zero intensity) occurs when the path difference S1P ~ S2P = (n + 1/2)λ, where n = 0, 1, 2, 3, …; at these points the waves arrive exactly out of phase and cancel.
For an arbitrary phase difference φ, the resultant intensity is I = 4I0 cos²(φ/2), which reduces to 4I0 for φ = 0, 2π, … and to 0 for φ = π, 3π, …

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Question 9

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Why do two independent sodium lamps illuminating two pinholes fail to produce a sustained interference pattern on a screen?

Light from an ordinary source like a sodium lamp undergoes abrupt, random phase changes at intervals of the order of 10⁻¹⁰ seconds, making each lamp an incoherent source.
Two independent lamps therefore have no fixed phase relationship — the phase difference between them changes randomly and rapidly with time, so no stable pattern of maxima and minima can be maintained.
The interference term averages to zero over the observation time, and only the sum of the individual intensities (I = 2I0) is observed uniformly across the screen.

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Question 10

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Explain how Young achieved two coherent sources in his double-slit experiment using a single source and two pinholes.

Young illuminated a single pinhole S with a bright source; the light spreading from S fell simultaneously on two closely spaced pinholes S1 and S2 on an opaque screen.
Since both S1 and S2 are derived from the same original source S, any abrupt phase change in S is manifested identically in the light from both S1 and S2, keeping their phase difference locked.
This phase-locking makes S1 and S2 behave as coherent sources, capable of producing a stable, observable interference fringe pattern on the screen GG′.

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Question 11

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Write the expression for the fringe width in Young's double-slit experiment and state how it changes if the separation between the slits is halved.

The fringe width β = λD/d, where λ is the wavelength of light, D is the distance from the slits to the screen, and d is the separation between the two slits.
If the slit separation d is halved (d → d/2), the fringe width doubles (β → 2β), because fringe width is inversely proportional to d.
Both bright and dark fringes are equally spaced with the same fringe width β, so halving d makes the entire fringe pattern twice as wide.

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Question 12

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How does the double-slit interference pattern differ from the single-slit diffraction pattern in terms of fringe width and intensity distribution?

In Young's double-slit experiment, bright and dark fringes are equally spaced with uniform intensity for the bright fringes (ignoring diffraction envelope), while single-slit diffraction gives a broad central maximum flanked by successively weaker secondary maxima.
The minima in single-slit diffraction occur at θ = nλ/a (n = ±1, ±2, …) and the central maximum has twice the angular width of any secondary maximum.
The actual double-slit pattern on a screen is a superposition (modulation) of the double-slit interference fringes by the single-slit diffraction envelope from each slit.

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Question 13

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State the condition for the minima in a single-slit diffraction pattern and explain why the central maximum is broader than secondary maxima.

Minima (zero intensity) in single-slit diffraction occur at angles θ ≈ nλ/a, where a is the slit width and n = ±1, ±2, ±3, … (n ≠ 0).
Secondary maxima occur approximately at θ ≈ (n + 1/2)λ/a and become progressively weaker with increasing n because the effective contribution from the slit decreases.
The central maximum extends from −λ/a to +λ/a (angular width 2λ/a), which is twice the angular width of any secondary maximum (λ/a), making it broader and much brighter.

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Chapter 10: Wave Optics | Short Questions

Define a wavefront and state the relationship between the direction of energy propagation and the wavefront.

State Huygens principle and explain how it accounts for the forward propagation of a wavefront while ruling out the backwave.

Using Huygens principle, explain why a plane wave incident on a convex lens produces a converging spherical wavefront on the other side.

What is the critical angle? Write the expression for the critical angle in terms of refractive indices and state the condition for total internal reflection.

Derive Snell's law of refraction using Huygens principle for a plane wave incident on an interface between two media.

When a light wave is refracted into a denser medium, which of the following change: speed, wavelength, frequency? Justify your answer.

State the superposition principle as applied to light waves and explain its role in the formation of an interference pattern.

Write the conditions for constructive and destructive interference in terms of path difference for two coherent sources vibrating in phase.

Why do two independent sodium lamps illuminating two pinholes fail to produce a sustained interference pattern on a screen?

Explain how Young achieved two coherent sources in his double-slit experiment using a single source and two pinholes.

Write the expression for the fringe width in Young's double-slit experiment and state how it changes if the separation between the slits is halved.

How does the double-slit interference pattern differ from the single-slit diffraction pattern in terms of fringe width and intensity distribution?

State the condition for the minima in a single-slit diffraction pattern and explain why the central maximum is broader than secondary maxima.

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