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In Young's experiment, the source is red light of wavelength \( 7 \times 10^{-7} \mathrm{~m} \). When a thin glass plate of refractive
\( \mathrm{P} \) index \( 1.5 \) at wavelength is put in the path of one of the

W interfering beams, the central bright fringe shifts by \( 10^{-3} \mathrm{~m} \) to the position previously occupied by the \( 5^{\text {th }} \) bright fringe. Find the thickness of the plate. When the source is now changed to green light of wavelength \( 5 \times 10^{-7} \mathrm{~m} \), the central fringe shifts to a position initially occupied by the \( 6^{\text {th }} \) bright fringe due to red light. Find the refractive index of glass for green light. Also estimate the change in fringe width due to the change in wavelength.
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