A thin equiconvex glass lens of refractive index 1.5 has power of 5D. When the lens is immersed in a liquid of refractive index n, it acts as a divergent lens of focal length 100cm. The value of n of liquid is
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formula of focal length is given by
1/f = (μ₂/μ₁ - 1)[1/R₁ - 1/R₂]
Here , 1/f = 5 D , μ₂ = 1.5 , μ₁ = 1
Then, 5 = (1.5/1 - 1)[1/R₁ - 1/R₂ ]
5 = (0.5)[ 1/R₁ - 1/R₂ ] ----------------------(1)
f = 100 cm = 1m, μ₂ = 1.5 , Let μ₁ = x
1/1 = (1.5/x - 1)[ 1/R₁ - 1/R₂ ]
1 = (1.5/x - 1)[ 1/R₁ - 1/R₂ ] ----------------(2)
divide equations (1) and (2),
5 = (0.5)/(1.5/x - 1)
7.5/x - 5 = 0.5
7.5/x = 5.5 ⇒x = 7.5/5.5 = 1.37
Hence, refractive index of liquid is 1.37
1/f = (μ₂/μ₁ - 1)[1/R₁ - 1/R₂]
Here , 1/f = 5 D , μ₂ = 1.5 , μ₁ = 1
Then, 5 = (1.5/1 - 1)[1/R₁ - 1/R₂ ]
5 = (0.5)[ 1/R₁ - 1/R₂ ] ----------------------(1)
f = 100 cm = 1m, μ₂ = 1.5 , Let μ₁ = x
1/1 = (1.5/x - 1)[ 1/R₁ - 1/R₂ ]
1 = (1.5/x - 1)[ 1/R₁ - 1/R₂ ] ----------------(2)
divide equations (1) and (2),
5 = (0.5)/(1.5/x - 1)
7.5/x - 5 = 0.5
7.5/x = 5.5 ⇒x = 7.5/5.5 = 1.37
Hence, refractive index of liquid is 1.37
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