Question

A ray of light is incident at the glass–water interface at an angle $i$, if it emerges finally parallel to the surface of the water, then the value of ${\mu }_g$ would be

• A. $\left(\frac{4}{3}\right)sini$
• B. $\frac{1}{sini}$
• C. $\frac{4}{3}$
• D. $1$

Answer 1

The correct option is (B) $\frac{1}{sini}$

Step 1, Given data

Ray of light is incident at the glass–water interface at an angle i.

Emerges parallel to the surface of the water.

Step 2, Finding the value

For Glass-Water surface

We know,

According to Snell's law

$\frac{sin\left(i\right)}{sin\left(r\right)}=\frac{{\mu }_w}{{\mu }_g}$

$\frac{sin\left(i\right)}{sin\left(r\right)}=\frac{4}{3{\mu }_g}$

For Water-Air interrface

$\frac{sin\left(r\right)}{sin\left({90}^{\circ }\right)}=\frac{3}{4}$

$sin\left(r\right)=\frac{3}{4}$

By substituting above equation

${\mu }_g=\frac{1}{sin\left(i\right)}$