In the figure, a broad beam of light of wavelength 632 nm is sent directly downw

Question

In the figure, a broad beam of light of wavelength 632 nm is sent directly downward through the top plate of a pair of glass plates touching at the left end. The air between the plates acts as a thin film, and an interference pattern can be seen from above the plates. Initially, a dark fringe lies at the left end, a bright fringe lies at the right end, and nine dark fringes lie between those two end fringes. The plates are then very gradually squeezed together at a constant rate to decrease the angle between them. As a result, the fringe at the right side changes between being bright to being dark every 15.5 s. (a) At what rate is the spacing between the plates at the right end being changed? (b) By how much has the spacing there changed when both left and right ends have a dark fringe and there are five dark fringes between them?

Explanation / Answer

a )Here for air film and normal incidence we have 2d = n

Initially, a dark fringe lies at the left end, a bright fringe lies at the right end, and nine dark fringes lie between those two end fringes. This implies n = 9.5

and later we have n ' = 9 in 2d' = n'

Then d - d' = (n/2) - n'/2

Here wavelength = 632 nm

Then change in spacing between the plates is d = d - d' = (632 nm/2)(9.5 - 9) = 158 nm

Now time interval t = 15.5 sec

Then rate of change of spacing between the plates is d/t = 158 nm / 15.5 s = 10.2 nm/s

b ) Now when both left and right ends have a dark fringe and there are five dark fringes between them then   n "= 6

Then   d - d" = (n/2) -(n"/2)

                    =( /2) ( n - n")

                    = (632 nm/2)(9.5- 6 )

                    = 1106 nm = 1.106 um

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