Light enters at an angle of incidence in a transparent rod of refractive index '$$n$$'. The least value of '$$n$$' for which the light once entered into it will not leave it through its lateral face whatsoever be the value of the angle of incidence is

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: