Optics 3 Question 39

39. A plano-convex lens has a thickness of 4cm. When placed on a horizontal table, with the curved surface in contact with it, the apparent depth of the bottom most point of the lens is found to be 3cm. If the lens is inverted such that the plane face is in contact with the table, the apparent depth of the centre of the plane face is found to be 25/8cm. Find the focal length of the lens. Assume thickness to be negligible while finding its focal length.

(1984, 6M)

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Answer:

Correct Answer: 39. μ1<μ2

Solution:

  1. Refer figure (a)

(a)

(b)

In this case refraction of the rays starting from O takes place from a plane surface. So, we can use

dapp =dactual μ or 3=4μ or μ=43

Refer figure (b) In this case refraction takes place from a spherical surface. Hence, applying

μ2vμ1u=μ2μ1R we have, 1(25/8)4/34=14/3R or 13R=13825=175R=25cm

Now, to find the focal length we will use the lens Maker’s formula

1f=(μ1)1R11R2=4311125=175f=75cm



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