In figure S is a monochromatic point source emitting light of wavelength `lambda = 500 nm` A thin lens of circular shape and focal length `0.10` m is cut into two identical havles `L_(1)` and `L_(2)` a plane passing through a diameter. The two havles are placed symmetrically about the central axis SO with a gap of `0.5` mm. The distance along the axis from S TO`L_(1)` and `L_(2)` is `0.15` m. The screen at O is normal to SO.
a. If the third intensity maximum occurs at point A on the screen, find the distance OA.
b. If the gap between, `L_(1)` and `L_(2)` is reduced from its original value of `0.5` mm, will the distance OA increase, decrease, or remain the same ?

Explanation

(a) 1mm, (b) increase