Question

Two thin symmetrical lenses one converging and other of diverging nature are made from different
material have equal radii of curvature R = 15 cm, the lenses are put in contact and immersed in water
(uy = 4/3). The focal length of the system in water is 30 cm. Then the difference between refractive
indices of the two lenses is
​

Answer 1

The difference between refractive  indices of the two lenses is 1/3.

Explanation:

Let f1 and f2 be focal length of the two lenses in water respectively.

1 / f1 = (μ1 / μw − 1)[1R + 1R] =(μ1 / μw − 1) 2 R -----(1)

1 / f2 = (μ2 / μw − 1)[−1 / R − 1 /R] = (μ2 / μw − 1) 2 R -----(2)

Adding (1) and (2)

1 / f1 + 1 / f2 = 1 / f = 2 ( μ1 − μ2) μwR

f - focal length of combination

1 / 30 = 2(μ1 − mu2) μwR  

μ1 − μ2 = μwR / 60

μ1 − μ2 = 4 × 15 / 3 × 60 = 1 / 3

μ1 = 2 / 3  

μ2 = 1 / 3

Thus the  difference between refractive  indices of the two lenses is 1/3.