During the derivation of Snell’s law using wavefront construction

PHYSICS · Single correct · CBSE · Physics · Wave Optics · Wave Optics

Problem

During the derivation of Snell’s law using wavefront construction, an incident wavefront

AB

in medium 1 (speed

v_1

) meets the interface at

A

first and at

B

later. After a time

t

, the secondary wavelet from

A

has radius

v_2 t

in medium 2 while the disturbance in medium 1 has advanced a distance

v_1 t

from

B

C

. Which of the following relations obtained from the geometry of the construction directly yields Snell’s law? (a)

\displaystyle \frac{\cos i}{\cos r}=\frac{v_1}{v_2}

(b)

\displaystyle \frac{\sin i}{\sin r}=\frac{v_1}{v_2}

(c)

\displaystyle \frac{\sin i}{\sin r}=\frac{v_2}{v_1}

(d)

\displaystyle \frac{\tan i}{\tan r}=\frac{v_1}{v_2}