Question

A ray of light is incident on a medium with angle of incidence $i$ and refracted into a second medium with angle of refraction $r$. The graph of $\sin \left(i\right)\text{vs}\sin \left(r\right)$ is shown in figure.
If the first medium is air, then the velocity of light in the second medium will be (Take $c=3\times {10}^8{\text{ms}}^{-1}$)

• A. $1.414\times {10}^8{\text{ms}}^{-1}$
• B. $1.732\times {10}^8{\text{ms}}^{-1}$
• C. $2.132\times {10}^8{\text{ms}}^{-1}$
• D. $1.532\times {10}^8{\text{ms}}^{-1}$

Answer 1

The correct option is B $1.732\times {10}^8{\text{ms}}^{-1}$

slope $=\tan {60}^{\circ }=\frac{\sin \left(i\right)}{\sin \left(r\right)}$
ie From snell's law
$\frac{\sin \left(i\right)}{\sin \left(r\right)}=\mu$
$\mu =\sqrt{3}=\frac{C}{v};v=\frac{C}{\sqrt{3}}=\frac{3\times {10}^8}{\sqrt{3}}=\sqrt{3}\times {10}^8{\text{ms}}^{-1}$
Speed of light in medium is $1.732\times {10}^8{\text{ms}}^{-1}$