A transparent solid cylindrical rod (refractive index $\frac{2}{\sqrt{3}}$ ) is kept in air. A ray of light incident on its face travels along the surface of the rod, as shown in figure. Calculate the angle $\theta$.

A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm . Calculate its magnifying power in normal adjustment and the distance of the image formed by the objective.

In the given figure the radius of curvature of curved face in the plano-convex and the plano-concave lens is $$15 \mathrm{~cm}$$ each. The refractive index of the material of the lenses is 1.5. Find the final position of the image formed.