CBSE Class 12 · 2017 · Wave OpticsShort Answer

A plane wavefront propagating from a rarer into a denser medium is incident at an angle of incidence

i

on a refracting surface. Draw a diagram showing the incident wavefront and the refracted wavefront. Hence verify Snell's law of refraction.

Answer: $\frac{sin i}{sin r} = \frac{v _{1}}{v _{2}} = μ$ , Snell's law.

Solution

Let a plane wavefront in the rarer medium (speed

v_{1}

) be incident at angle

i

on the interface

P P^{'}

, and let the refracted wavefront in the denser medium (speed

v_{2}

) make angle

r

.
In time

τ

the disturbance at one end travels

B C = v_{1} τ

to reach the surface, while the secondary wavelet from the other end spreads

A E = v_{2} τ

into the denser medium. Drawing the two right triangles sharing the hypotenuse

A C

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 = constant

\frac{sin i}{sin r} = μ

Since

v_{2} < v_{1}

(denser medium),

r < i

, so the refracted ray bends towards the normal, as expected.

CBSE Class 12 Board · 2017 · Subjective