Question

Light is incident from air on oil at an angle of ${30}^{\circ }$. After moving through oil-1 and another medium; oil-2, it enters glass and then it enters the water. If the refractive indices of glass and water are $1.5$ and $1.3$, respectively, find the angle which the ray makes with normal in water.

• A. $si{n}^{-1}\left(\frac{1}{2.4}\right)$
• B. $si{n}^{-1}\left(\frac{1}{2.5}\right)$
• C. $si{n}^{-1}\left(\frac{1}{2.6}\right)$
• D. $si{n}^{-1}\left(\frac{1}{2.8}\right)$

Answer 1

The correct option is C

$si{n}^{-1}\left(\frac{1}{2.6}\right)$

As we know
$\mu \text{sin}i=\left(\text{constant}\right)\Rightarrow \mu \text{sin}{i}_{\text{air}}={\mu }_{\text{water}}\text{sin}{r}_{\text{water}}$
$\text{sin}30=1.3\text{sin}r$

$\text{sin}r=\frac{1}{2\times 1.3}=\frac{1}{2.6};r={\text{sin}}^{-1}\left(\frac{1}{2.6}\right)$