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Question: Answered & Verified by Expert
A planoconvex lens has thickness of 4 cm. 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 3 cm. 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 258 cm. The focal length of the lens is (assume thickness of lens to be negligible)
PhysicsRay OpticsBITSATBITSAT 2018
Options:
  • A 85 cm
  • B 59 cm
  • C 75 cm
  • D 7.5 cm
Solution:
2749 Upvotes Verified Answer
The correct answer is: 75 cm

In first case refraction of the rays, takes place from a plane surface, so we can use dapp=dactual μ

3=4μμ=43

where, dapp  and dactual = apparent and real depth, respectively.

Now, in second case, as from Fig. (b), refraction takes place from a spherical surface, so

μ2v-μ1u=μ2-μ1Rm

or 1(-25/8)-4/3(-4)=1-4/3-R

or 13R=13-825=175

R=25 cm

Now, using Lens' Makers formula, to calculate focal length

1f=μ-11R1-1R2

1f=43-11-1(-25)=175

f=75 cm

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