Define refractive index of a medium.
or
How is the refractive index of an optical medium related to the speed of light in that medium? 

Refractive index of a medium for a light of given wavelength may be defined as the ratio of the speed of light in vacuum to  the speed of light in that medium.

Mathematically, it is given by

Refractive index = Speed of light in vacuumSpeed of light in medium = cv
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Which spherical mirror has (i) a real focus and (ii) a virtual focus?

(i) A concave mirror has a real focus.
(ii) A convex mirror has a virtual focus.

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Why is a concave mirror preferred to a plane mirror for shaving?

A concave mirror is preferred as a shaving mirror because it forms a magnified and erect image of the face when the mirror is brought closer to tha face.
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A concave mirror is held in water. What should be the change in the focal length of the mirror?

The focal length of a concave mirror does not depend on the nature of the surrounding medium. So, there won't be any change in the focal length of the concave mirror when, held in water. 
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Can we photograph a virtual image?


Yes, a virtual image can be photographed because the rays diverging from the virtual image are real and can be focussed on a screen.
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