Question

A laser beam is incident on the end face of a cylindrical rod at an angle of 51° to the normal. The refractive index of the rod is 1.49 and its diameter is 30cm. If the length of the rod is 50cm, how many internal reflections does the laser beam experience before it exists the rod?

Answer 1

As per the given question,

Let the angle of refraction is r

so applying Snell's rule,

$\frac{\sin 51^o}{\sin r}=1.49$

$\Rightarrow \sin r = \frac{\sin 51^o}{1.49}$

$\Rightarrow \sin r= 0.52$

$\Rightarrow r= \sin^{-1}(0.52) =31.33^o$

Let the the first reflection will take place at x distance from the one end of the cylinder.

$\Rightarrow \tan 31.33^o =\frac{15}{x}$

$\Rightarrow x = \frac{15}{\tan 31.33^o}$

$\Rightarrow x = 24.4 cm$

Hence, number of reflection inside the cylindrical tube $n\times 24.6 = 50 cm$

$n = \frac{50}{24.6}\sim2$

Hence, ray will reflect at least 2 times inside the cylindrical tube.