Question

A lens made of glass. (u=1.5) has a focal length 80 CM when immersed in a transparent liquid of refractive index 1.3. find the focal length of the lens in air ​

Answer 1

focal length of lens in air is 24.64 (approximately)

refractive index of glass, μ_g = 1.5

refractive index of transparent liquid, μ_l = 1.3

focal length of lens in liquid medium, F = 80cm

using forming, 1/f = (μ - 1)[1/R1 - R2]

let focal length of lens in air medium is f

so, 1/f = (1.5 - 1) [1/R1 - 1/R2]

or, 1/f = 0.5 [1/R1 - 1/R2].. ......(1)

focal length of lens in liquid medium is F = 80 cm

so, 1/F = 1/80cm = (μ_g/μ_l - 1)[1/R1 - 1/R2]

⇒1/80 = (1.5/1.3 - 1) [1/R1 - 1/R2]

⇒1/80 = 0.154 [1/R1 - 1/R2] ......(2)

from equations (1) and (2),

80/f = 0.5/0.154

⇒f = 80 × 0.154/0.5 = 24.64 cm

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Answer 2

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refractive index of glass, μ_g = 1.5

refractive index of transparent liquid, μ_l = 1.3

focal length of lens in liquid medium, F = 80cm

using forming, 1/f = (μ - 1)[1/R1 - R2]

let focal length of lens in air medium is f

so, 1/f = (1.5 - 1) [1/R1 - 1/R2]

or, 1/f = 0.5 [1/R1 - 1/R2].. ......(1)

focal length of lens in liquid medium is F = 80 cm

so, 1/F = 1/80cm = (μ_g/μ_l - 1)[1/R1 - 1/R2]

⇒1/80 = (1.5/1.3 - 1) [1/R1 - 1/R2]

⇒1/80 = 0.154 [1/R1 - 1/R2] ......(2)

from equations (1) and (2),

80/f = 0.5/0.154

⇒f = 80 × 0.154/0.5 = 24.64 cm