Question

A transparent cylinder of radius 2 m has a mirrored surface on its right half as shown in the figure. A light ray travelling in air is incident on the left side of the cylinder. The incident ray and exiting ray are parallel to each other and at a distance of 2 m. Choose the INCORRECT options :

• A. Angle of incidence is ${30}^0$
• B. Angle of deviation due to reflection at mirror is ${150}^0$
• C. Refractive index of material of cylinder is 2 cos${15}^0$
• D. None of these

Answer 1

The correct option is C Refractive index of material of cylinder is 2 cos${15}^0$

If S be the angular deviation produced by the cylinder and mirror combination, then based on geometrical considerations,
$\pi =i-r+\pi -2r+i-r$

Where, $i$ = angle of incidence,

$r$ = angle of refraction

This gives a relation between $i$ and $r$ as $i=2r$

Now, with the angle of incidence $={30}^0$, the angle of refraction $={15}^0$

So, the refractive index $=\frac{sini}{sinr}$

Thus, $m=\frac{1}{2sin15}$