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Ray Optics And Optical Instruments

Question
CBSEENPH12047698

The radius of the convex surface of planoconvex lens is 20 cm and the refractive index of the material of the lens is 1.5. The focal length is

  • 30cm

  • 50 cm

  • 30 cm

  • 40 cm

Solution

D.

40 cm

For refraction through a spherical interface (from medium 1 to 2 of refractive index n1 and nrespectively)

n2ν - n1μ= n2-n1RThin lens formula1μ - 1ν = 1f

Lens maker formula

1f =  n2-n1n1 1R1-1R2

Using the relation for focal length of planoconvex lens

=1f= μ - 1 1R1 - 1R2Refractive index of material of lens  μ=1.5 cm, R1=20 cm  and R2=1f = 1.5 - 1 120 - 11f = 140or  f  = 40 cm