PhysicsCBSE Class 12 · Board exam 2023, set 55/1/1 · 2 marks · Very short answer

CBSE Class 12 Physics 2023: question 21(a)

Set in the CBSE Class 12 board exam of 2023, paper 55/1/1, section B, question 21(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(a) · 2 marks · Very short answerWave Optics

Using Huygens' principle, draw a ray diagram showing the propagation of a plane wave refracting at a plane surface separating two media. Also verify Snell's law of refraction.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 55/1/1.

Hints

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

Hint 1

Let the wavefront take time $τ$ to cover the extra distance BC in medium 1.

Hint 2

Draw a secondary wavelet from A in medium 2 of radius $v_{2} τ$ and a tangent from C.

Hint 3

Use the two right triangles sharing hypotenuse AC.

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.

Ray diagram (described): a plane surface PP′ separates medium 1 (speed $v_{1}$ , upper) and medium 2 (speed $v_{2}$ , lower, $v_{2} < v_{1}$ ). Plane incident wavefront AB meets the surface at A, making angle $i$ with it. In time $τ$ , the disturbance from B travels BC $= v_{1} τ$ to reach C on the surface. From A, a secondary wavelet of radius AE $= v_{2} τ$ is drawn in medium 2. The tangent CE from C to this sphere is the refracted wavefront, making angle $r$ with the surface. Rays are drawn perpendicular to AB and CE.
1 mark
In right triangle ABC: $sin i = \frac{B C}{A C} = \frac{v _{1} τ}{A C}$ ; in right triangle AEC: $sin r = \frac{A E}{A C} = \frac{v _{2} τ}{A C}$
½ mark
Dividing: $\frac{sin i}{sin r} = \frac{v _{1}}{v _{2}} = \frac{c / n _{1}}{c / n _{2}} = \frac{n _{2}}{n _{1}} = n_{21}$ , a constant — this is Snell's law ( $n_{1} sin i = n_{2} sin r$ ).
½ mark

Answer: $\frac{sin i}{sin r} = \frac{v _{1}}{v _{2}} = n_{21}$ (Snell's law verified)

Where the marks are

Correct Huygens construction with incident wavefront AB, wavelet of radius $v_{2} τ$ and refracted wavefront CE (1 mark)
Writes $sin i = v_{1} τ / A C$ and $sin r = v_{2} τ / A C$ (½ mark)
Obtains $sin i / sin r = v_{1} / v_{2} = n_{21}$ (½ 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 paper2023 board paper, set 55/1/1: every question, by section.

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CBSE Class 12 Physics 2023: question 21(a)

Hints

Step-by-step solution

Revise the chapter

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