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 halves` L_(1) `and` L_(2)` by a plane passing through a doameter. The two halves are placed symmetrically about the central axis SO with a gap of 0.5 mm. The distance along the axis from A to `L_(1) `and `L_(2) is 0.15 m`, while that from` L_(1)` and` L_(2)` to O is 1.30 m. The screen at O is normal to SO.
(a) If the `3^(rd) `intensity maximum occurs at point P on screen, find distance OP.

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 halves L_(1) and L_(2) by a plane passing through a doameter. The two halves are placed symmetrically about the central axis SO with a gap of 0.5 mm. The distance along the axis from A to L_(1) and L_(2) is 0.15 m , while that from L_(1) and L_(2) to O is 1.30 m. The screen at O is normal to SO. (b) If the gap between L_(1) and L_(2) is reduced from its original value of 0.5 mm, will the distance OP increases, devreases or remain the same?

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