Ray optics problem with glass slab and mirror

Question

A 20 cm thick glass slab of refractive index 1.5 is kept in front of a mirror. Find the position of the image relative to the mirror as seen by an observer through the glass slab when a point object is kept in air at a distance of 40 cm from the mirror.[Ans:80/3]

How do u solve it?...method?...

Answer 1

I am assuming it is plane mirror.

First find the position of the image only because of the mirror. Then treat that image as object and find its image because of the glass slab.

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Answer 2

The thickness T of the slab appears reduced to T/N, thus there is an apparent thickness reduction of T - T/N or in this case T/3 or 6.666 cm. In a double passage through the slab, the total distance reduction is 2T/3 or 13.333 cm. Assuming the observer sees the mirror surface directly, not through the slab, the apparent distance of the point is 40 - 13.333 = 26.666 = 80/3 cm from the mirror.