Question

Light enters a transparent rod of refractive index n. For what value of refractive index of the material of the rod, the light once entered into it will not leave it through its lateral face whatsoever be the angle of incidence ?

• A. $n>\sqrt{2}$
• B. $n=1$
• C. $n=1.1$
• D. $n=1.3$

Answer 1

The correct option is A $n>\sqrt{2}$

For total internal reflection to take place at all times,

$sin{r}_1>\frac{1}{n}$

Hence $n>\frac{1}{sin{r}_1}$

Also from Snell's law, $sin\left(i\right)=nsinr$

$r+r_1=\pi$

Therefore $sini=ncos{r}_1$

$n>\frac{1}{{\sqrt{1-\left(\frac{sin\left(i\right)}{n}\right)}}^2}$

$n^2>1+si{n}^{2}i$

Maximum value of $sini$ can be 1.

Hence, $n>\sqrt{2}$