Question

A ray of light is incident at an angle i on a glass slab of refractive index $\mu$. The angle between reflected and refracted light is ${90}^o$. Then the relationship between i and $\mu$ is.

• A. $i=ta{n}^{-1}\left(\frac{1}{\mu }\right)$
• B. $tani=\mu$
• C. $sini=\mu$
• D. $cosi=\mu$

Answer 1

The correct option is B $tani=\mu$

Let the angle of reflection and refraction be $r_1,r_2$ respectively.

Since angle between reflected and refracted ray is ${90}^{\circ }$,

$r_1+r_2={90}^{\circ }$.

From law of reflection, $r_1=i$

From Snell's law,

$sini=\mu sin{r}_2$

$=\mu sin({90}^{\circ }-r_1)$

$=\mu cos{r}_1=\mu cosi$

$⟹tani=\mu$