IIT 1993 | Interference Pattern Due To Split Lens | Fringe Width Calculation

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In given figure, S is a monochromatic point
source emitting light of wavelength λ= 500 nm. A thin
lens of circular shape and focal length 0.10 m is cut
into two identical halves L1 and L2 by a plane passing
through a diameter. The two halves are placed symmetrically about the central axis SO with a gap of 0.5 mm.
The distance along the axis from S to L1 and L2 is
0.15 m while that from L1 and L2 to O is 1.30 m. The
screen at O is normal to SO
(a) If the third intensity maximum occurs at the point
A on the screen, find the distance OA.
(b) If the gap between L1 and L2 is reduced from its
original value of 0.5 mm, will the distance OA increase, decrease, or remain the same.

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