PhysicsCBSE Class 12 · Sample paper, session 2023-24 · 5 marks · Long answer

CBSE Class 12 Physics sample paper 2023-24: question 31(b)

From the official CBSE sample question paper for 2023-24, section E, question 31(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q31(b) · 5 marks · Long answerWave Optics

i. Define a wavefront. How is it different from a ray?
ii. Using Huygens's construction of secondary wavelets draw a diagram showing the passage of a plane wavefront from a denser to a rarer medium. Using it verify Snell's law.
iii. In a double slit experiment using light of wavelength 600nm and the angular width of the fringe formed on a distant screen is 0.1°. Find the spacing between the two slits.
iv. Write two differences between interference pattern and diffraction pattern.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

Open one hint at a time and try again before the next.

Hint 1

A wavefront joins points of equal phase; rays are perpendicular to it.

Hint 2

In the same time, the wavelet in the rarer medium travels farther; compare BC and AE using right triangles with common hypotenuse AC.

Hint 3

Convert 0.1° to radians before using $θ = λ / d$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) A wavefront is the locus of all points of the medium vibrating in the same phase (a surface of constant phase). A ray shows the direction in which the wave travels, whereas a wavefront is a surface; the ray at any point is always normal to the wavefront at that point.
1 mark
(ii) Diagram (described): A plane wavefront AB in the denser medium 1 (speed $v_{1}$ ) meets the boundary XY obliquely at angle of incidence i, end A touching first. In time t, the wavelet from B reaches C on the boundary: $B C = v_{1} t$ . In the same time, a secondary wavelet from A spreads into the rarer medium 2 with radius $A E = v_{2} t$ (larger, since $v_{2} > v_{1}$ ). The tangent CE drawn from C to this wavelet is the refracted wavefront; the refracted ray bends away from the normal ( $r > i$ ).
1 mark
From triangles ABC and AEC: $sin i = \frac{B C}{A C}$ , $sin r = \frac{A E}{A C}$
$\Rightarrow \frac{sin i}{sin r} = \frac{B C}{A E} = \frac{v _{1} t}{v _{2} t} = \frac{v _{1}}{v _{2}} =$ constant. With $n = c / v$ , this gives $n_{1} sin i = n_{2} sin r$ , which is Snell's law.
1 mark
(iii) Angular fringe width $θ = \frac{λ}{d}$ . $θ = 0. 1^{\circ} = 0.1 \times \frac{π}{180} = 1.745 \times 1 0^{- 3}$ rad.
$d = \frac{λ}{θ} = \frac{6 \times 1 0 ^{- 7}}{1.745 \times 1 0 ^{- 3}} = 3.4 \times 1 0^{- 4}$ m (≈ 0.34 mm).
1 mark
(iv) Differences: (1) Interference results from superposition of waves from two coherent sources; diffraction results from superposition of wavelets from different parts of the same wavefront. (2) In interference all bright fringes have nearly equal width and intensity; in diffraction the central maximum is twice as wide as the others and intensity of successive maxima falls sharply.
1 mark

Answer: (iii) Slit spacing ≈ $3.4 \times 1 0^{- 4}$ m; Snell's law $sin i / sin r = v_{1} / v_{2}$ verified

Where the marks are

Definition of wavefront and its difference from a ray (1 mark)
Huygens construction diagram for denser to rarer refraction (1 mark)
Shows $sin i / sin r = v_{1} / v_{2}$ = constant (1 mark)
Uses $θ = λ / d$ with θ in radians to get $d = 3.4 \times 1 0^{- 4}$ m (1 mark)
Two correct differences between interference and diffraction patterns (1 mark)

Revise the chapter

Chapter: Wave Optics (notes, formulas, where marks are lost and every past question)
Topic: Huygens Principle and Wavefronts

Practise this chapterBoard-style questions from Wave Optics, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24: every question, by section.

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CBSE Class 12 Physics sample paper 2023-24: question 31(b)

Hints

Step-by-step solution

Revise the chapter

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