In the normal adjustment of an astronomical telescope, the objective and eyepiece are $$32 \mathrm{~cm}$$ apart. If the magnifying power of the telescope is 7, find the focal lengths of the objective and eyepiece.

When a particular wave length of light is used the focal length of a convex mirror is found to be $$10 \mathrm{~cm}$$. If the wave length of the incident light is doubled keeping the area of the mirror constant, the focal length of the mirror will be:

For a $$30^{\circ}$$ prism when a ray of light is incident at an angle $$60^{\circ}$$ on one of its faces, the emergent ray passes normal to the other surface. Then the refractive index of the prism is:

A ray of light travelling through a medium of refractive index $$\frac{5}{4}$$ is incident on a glass of refractive index $$\frac{3}{2}$$. Find the angle of refraction in the glass, if the angle of incidence at the given medium - glass interface is $$30^{\circ}$$.