To a fish under water, viewing obliquely, a fisherman standing on the bank of a lake looks

In a container of height $$21 \mathrm{~cm}$$, certain transparent liquid is taken to a height of $$12 \mathrm{~cm}$$. When seen from above, it appears half filled. The refractive index of the liquid is

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.