Please solve this question on refraction.

Question

A t cm thick glass (R.I. = n) slab is silvered at one of the surfaces to form a plane mirror. A point object is placed at a distance of u cm from the unsilvered face. What will the image distance from the unsilvered distance be?

Answer 1

Let

1)I₁ is the image formed by refraction from P_1.

2)I₂ is the image formed by reflection from P_2.

3)I₃ is the image formed by again refraction from P_1.

Location of Image I₁

1/p = -n/I₁ ; so, I₁ = -n.p from P₁
-n.p + t from P₂

Location of the image I₂

-n.p + t behind the mirror or -n.p + t +t from P1

Location of the image I₃

n/ (-n.p + t +t) = 1/x
x = (2t - np)/n

Thus (2t - np)/n is the final image position w.r.t P₁.