A concave mirror of radius R is kept on a horizontal table(see inserted image). Water(refractive index=mu) is poured into it up to a height h. Where should an object be placed so that its image is formed on itself?

 

 

 

 

The radius of curvature of concave mirror is R. Water is poured upto height h.

 

Now, if the object is placed at the centre of curvature (C) of the mirror, then the image is formed on itself, i.e. on C.

 

But, since water of refractive index μ is poured in it, the object should be placed closer to the surface of water than C.

That is, the object should be placed at O. Let x be the distance from the surface of water.

 

Now, we have