Question

Rays of light fall on a glass plate of refractive index $=\sqrt{3}$. If the angle between refracted ray and reflected ray is $90$, the angle of incidence is :

• A. $90$
• B. $45$
• C. $135$
• D. $60$

Answer 1

The correct option is D $60$

From Snell's law,

$1\sin i=\sqrt{3}\sin r_2$

$r_2={\sin }^{-1}\left(\frac{1}{\sqrt{3}}\sin i\right)$

and we can observe that

$r_1+{90}^0+r_2={180}^0$

$r_1+r_2={90}^0$

and $r_1=i$ [by law of reflection]

So $i+{\sin }^{-1}\left(\frac{1}{\sqrt{3}}\sin i\right)={90}^0$

$\sin (i+{\sin }^{-1}(\frac{1}{\sqrt{3}}\sin i\left)\right)=1$

$\sin i\cos \left({\sin }_{-1}\right(\frac{1}{\sqrt{3}}\sin i\left)\right)+\cos i\left(\frac{1}{\sqrt{3}}\right)\sin i=1$

After solving the equation
we get $i={60}^0$