Question

A bicovex lens of refractive index 1.5 having focal length 0.2m acts as a divergent lensof power1d. When immersed in a liquid.Find refractive index of liquid

Answer 1

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.



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