Question

A wave front AB in air is incidental on plane glass surface XY, as given in figure. Its position CD after refraction through a glass shown along with normal drawn as A and D. The refrac tive index of glass w.r.t. air is given by

• A. $\frac{sin\theta }{sin\varphi }$
• B. $\frac{sin\varphi }{sin\theta }$
• C. $\frac{sin2\theta }{sin\varphi }$
• D. $\frac{sin\theta }{sin{\varphi }^{\prime }}$

Answer 1

Answer: (D)

$\frac{sin\theta }{sin{\varphi }^{\prime }}$

$\begin{array}{c}\text{We know that refractive index is directly proportional}\\ \text{to speed of light in that time.}\end{array}$

$\begin{array}{c}\text{So}\frac{{\mu }_{\text{glass}}}{{\mu }_{\text{air}}}=\frac{BD}{AC}\\ \text{we know that}\angle B=LC={40}^{\circ }\\ \text{So}In△ABD=AD\sin \theta \\ \text{In}△ACDAC=AD\sin {\varphi }^{\prime }\end{array}$

$\begin{array}{c}\text{So}{\mu }_{\text{rel}}=\frac{sin\theta }{\sin {\varphi }^{\prime }}\\ \text{OPTION "D" is correct.}\end{array}$