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Question:

A planoconvex lens becomes an optical system of 28cm focal length when its plane surface is silvered and illuminated from left to right. If the same lens is instead silvered on the curved surface and illuminated from the other side, it acts like an optical system of focal length 10 cm. What is the refractive index of the material of the lens?

1.50

1.51

1.55

1.75

Solution:

Effective focal length of the combination, 1/F = 1/2f + 1/fm
fm → ∞
This gives, f = 56
fm = R/2
Hence, 1/F = 1/2f + 2/R
This gives, R = 31.11
f = (μ-1)(1/R)
μ = 1.55