Water is poured into a concave mirror of radius of curvature R up to a height h. An object is placed along the principal axis at a distance x above the level of the water. What should be the value of x so that the image of the object is formed on itself?
For an image to be formed on itself the object must be placed at the centre of curvature of the concave lens.
Since water has been poured into the mirror, the optical length in the medium (water) is Mu*h (where Mu = refractive index of water).
The Attempt at a Solution
Object distance from the pole of the mirror = x + Mu*h
Or R = x + Mu*h
Or x = R - Mu*h
Since the answer given in the book is x = (R - h) / Mu, I am unable to figure out as to where I have gone wrong. Would request for help. Thanks.