CBSE Class 12 · 2016 · All India · Wave OpticsShort Answer

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(i) Derive Snell's law on the basis of Huygens' wave theory when light is travelling from a denser to a rarer medium.
(ii) Draw sketches to differentiate between a plane wavefront and a spherical wavefront.

Solution

(i) Let

A B

be a plane wavefront incident at angle

i

on the interface

X Y

separating a denser medium (speed

c_{1}

) from a rarer medium (speed

c_{2}

). While the disturbance at

A

travels to

A^{'}

in time

t

with

A A^{'} = c_{1} t

, the disturbance from

B

spreads into the rarer medium as a secondary wavelet of radius

B B^{'} = c_{2} t

. The tangent

A^{'} B^{'}

from

A^{'}

to this wavelet is the refracted wavefront, making angle

r

with the surface.

In △ A B A^{'} : sin i = \frac{A A ^{'}}{B A ^{'}} = \frac{c _{1} t}{B A ^{'}}

In △ A^{'} B^{'} A : sin r = \frac{B B ^{'}}{B A ^{'}} = \frac{c _{2} t}{B A ^{'}}

∴ \frac{sin i}{sin r} = \frac{c _{1}}{c _{2}} =_{1} n_{2} = constant

\frac{sin i}{sin r} =_{1} n_{2}

which is Snell's law of refraction.
(ii) See the sketches: a

plane wavefront

consists of parallel plane surfaces with rays parallel to one another (a source at large distance), while a

spherical wavefront

consists of concentric spherical surfaces with rays radiating from (or converging to) a point source.

CBSE Class 12 Board · 2016 · All India · Subjective

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CBSE Class 12 · 2016 · All India · Wave OpticsShort Answer

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