A concave mirror of radius R is kept on a horizontal table. 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 ?

Explanation

If object are formed at the same place, for this after refraction by liquid rays must be incident normally on the mirror i.e., after refraction rays must pass through centre of curvature of mirror hence image after refraction must be formed at centre of curvature of mirror.
Refraction at plane surface:
`mu_1=1,mu_2=-x,v=-(R-h)`
`(mu_2)/(v)-(mu_1)/(u)=0`
`(mu)/(-(R-h))-(1)/(-x)=0`
`x=(R-h)/(mu)`
Distance of object above water surface `=(R-h)/(mu)`