CBSE Class 12 · Wave OpticsLong Answer

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(a) (i) A plane light wave propagating from a rarer into a denser medium is incident at an angle 'i' on the surface separating the two media. Using Huygens' 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.

Answer: (i) $\frac{sin i}{sin r} = \frac{v _{1}}{v _{2}} = μ$ .
(ii) $y = 10.5$ mm.

Solution

(a)(i) By Huygens' construction, while the end of the incident wavefront travels

B C = v_{1} τ

in the rarer medium to reach the interface, the secondary wavelet from the other end spreads

A E = v_{2} τ

into the denser medium. With

A C

the common line,

sin i = \frac{B C}{A C} = \frac{v _{1} τ}{A C}, sin r = \frac{A E}{A C} = \frac{v _{2} τ}{A C}

∴ \frac{sin i}{sin r} = \frac{v _{1}}{v _{2}} = μ

\frac{sin i}{sin r} = μ

(ii) The

n^{th}

dark fringe is at

y = \frac{( 2 n - 1 )}{2} \frac{λ D}{d}

. For

n = 4

d = 0.30 \times 1 0^{- 3}

D = 1.5

λ = 600 \times 1 0^{- 9}

y = \frac{7}{2} \cdot \frac{600 \times 1 0 ^{- 9} \times 1.5}{0.30 \times 1 0 ^{- 3}} = \frac{7}{2} \times 3 \times 1 0^{- 3} = 1.05 \times 1 0^{- 2} m

y = 10.5 mm

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CBSE Class 12 · Wave OpticsLong Answer

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