A thin walled glass container is filled with water ( μ = 3 4 ) . A point source S is fixed inside water. A thin equiconvex lens ( μ = 1.5 ) and concave mirror are arranged with mutual separation R/2

Question

A thin walled glass container is filled with water ( μ = 3 4 ​ ) . A point source S is fixed inside water. A thin equiconvex lens ( μ = 1.5 ) and concave mirror are arranged with mutual separation R/2 as shown in figure. If the distance of the source from the point A is 3 2 R ​ , the separation between the source and final image as seen by an observer at the position of S is nR/6, find n. All curved surfaces of lens and mirror have radius of curvature R.

TestHub · Accepted Answer

Refraction at the plane water surface places the apparent source at $\frac{2 R /3}{4/3} = \frac{R}{2}$ from A, i.e. at distance R from the lens.

The lens ( $\frac{1}{f} = (1.5 - 1) \frac{2}{R}$ , so $f = R$ ) makes the beam parallel; the mirror ( $f = \frac{R}{2}$ ) focuses it back at the lens plane, so the returning image lies $\frac{R}{2}$ right of A.

The observer in water sees this at $\frac{4}{3} \times \frac{R}{2} = \frac{2 R}{3}$ right of A; separation from S is $\frac{2 R}{3} + \frac{2 R}{3} = \frac{4 R}{3} = \frac{8 R}{6}$ , so n = 8.

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