Answer the following. (i) A plane light wave propagating from a rarer into a denser medium, is incident at an angle i on the surface separating two media. Using Huygen's principle, draw the refracted wave and hence verify Snell's law of refraction. (ii) In a Young's double slit experiment, the slits are separated by 0.30 mm and the screen is kept 1.5 m away. The wavelength of light used is 600 nm. Calculate the distance between the central bright fringe and the 4^th dark fringe.

(i) n_1 i = n_2 r (Snell's law verified); (ii) 1.05×10^-2 m (10.5 mm)

PhysicsCBSE Class 12 · Board exam 2024, set 55/5/1 · 5 marks · Case-based

CBSE Class 12 Physics 2024: question 33(a)

Set in the CBSE Class 12 board exam of 2024, paper 55/5/1, section E, question 33(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(a) · 5 marks · Case-basedCompetency-basedWave Optics

Answer the following.

(i)
A plane light wave propagating from a rarer into a denser medium, is incident at an angle i on the surface separating two media. Using Huygen's principle, draw the refracted wave and hence verify Snell's law of refraction.
0 marks
(ii)
In a Young's double slit experiment, the slits are separated by 0.30 mm and the screen is kept 1.5 m away. The wavelength of light used is 600 nm. Calculate the distance between the central bright fringe and the $4^{t h}$ dark fringe.
0 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 55/5/1.

Hints

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

Hint 1

In the time the wave travels BC in the rarer medium, how far does the secondary wavelet from A travel in the denser medium?

Hint 2

Both right triangles share the hypotenuse AC; write $sin i$ and $sin r$ using it and divide.

Hint 3

For (ii), dark fringes lie at odd multiples of half the fringe width $β = λ D / d$ ; for the 4th dark fringe use $(2 n - 1) /2 = 3.5$ .

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) Diagram: Let the surface PP′ separate medium 1 (rarer, speed $v_{1}$ ) from medium 2 (denser, speed $v_{2} < v_{1}$ ). The incident plane wavefront AB meets the surface at A at angle $i$ . In time $τ$ , the disturbance at B travels to C, so $B C = v_{1} τ$ . With A as centre, draw a sphere (arc) of radius $A E = v_{2} τ$ in medium 2. Draw the tangent CE from C to this arc. CE is the refracted wavefront, and it makes angle $r$ with the surface. Since $v_{2} < v_{1}$ , it bends towards the normal.
1 mark
In right triangle ABC (right angle at B): $sin i = \frac{B C}{A C} = \frac{v _{1} τ}{A C}$ ...(1)
½ mark
In right triangle AEC (right angle at E): $sin r = \frac{A E}{A C} = \frac{v _{2} τ}{A C}$ ...(2)
½ mark
Dividing (1) by (2): $\frac{sin i}{sin r} = \frac{v _{1}}{v _{2}}$ ...(3)
½ mark
Using $n_{1} = \frac{c}{v _{1}}$ and $n_{2} = \frac{c}{v _{2}}$ : $\frac{sin i}{sin r} = \frac{n _{2}}{n _{1}}$ , i.e. $n_{1} sin i = n_{2} sin r$ . This is Snell's law of refraction.
½ mark
(ii) The $n$ th dark fringe is at $x_{n} = (2 n - 1) \frac{λ D}{2 d}$ . Here $n = 4$ , $λ = 600 \times 1 0^{- 9}$ m, $D = 1.5$ m and $d = 0.30 \times 1 0^{- 3}$ m.
1 mark
Substituting: $x_{4} = \frac{7 \times 600 \times 1 0 ^{- 9} \times 1.5}{2 \times 0.30 \times 1 0 ^{- 3}} = 7 \times 1.5 \times 1 0^{- 3} = 1.05 \times 1 0^{- 2}$ m $= 10.5$ mm.
1 mark

Answer: (i) $n_{1} sin i = n_{2} sin r$ (Snell's law verified); (ii) $1.05 \times 1 0^{- 2}$ m (10.5 mm)

Where the marks are

Correct Huygens construction showing incident wavefront AB, $B C = v_{1} τ$ , arc 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 + ½ marks)
Obtains $sin i / sin r = v_{1} / v_{2}$ (½ mark)
Uses $n = c / v$ to get $n_{1} sin i = n_{2} sin r$ (½ mark)
Uses dark fringe formula $x = (2 n - 1) λ D /2 d$ with $n = 4$ (1 mark)
Correct substitution and result $1.05 \times 1 0^{- 2}$ m (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 paper2024 board paper, set 55/5/1: every question, by section.

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CBSE Class 12 Physics 2024: question 33(a)

Hints

Step-by-step solution

Revise the chapter

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