Question

The focal length of a lens are in the ratio 13:8 when it is immersed in two
different liquids of refractive indices 1.3 and 1.2 respectively. The refractive
index of the material of the lens is​

Answer 1

Let refractive index of the material of the lens is μ.

using formula,

1/f = (μrel - 1) [1/R1 - 1/R2]

given, ratio of focal length of lens are in the ratio 13 : 8.

so, focal length of first lens = 13f

and focal length of 2nd lens = 8f

for first lens,

1/13f = (μ/1.3 - 1)[1/R1 - 1/R2] ....(1)

for 2nd lens,

1/8f = (μ/1.2 - 1) [1/R1 - 1/R2] ....(2)

from equations (1) and (2),

8/13 = (μ/1.3 - 1)/(μ/1.2 - 1)

or, 8/13 = 1.2(μ - 1.3)/1.3(μ - 1.2)

or, 8(μ - 1.2) = 12(μ - 1.3)

or, 2μ - 2.4 = 3μ - 3.9

or, μ = 1.5

hence, refractive index of lens is 1.5