Two rectangular glass plates (n = 1.60) are in contact along one edge and are se

Question

Two rectangular glass plates (n = 1.60) are in contact along one edge and are separated along the opposite edge (figure below). Light with a wavelength of 645 nm is incident perpendicularly onto the top plate. The air between the plates acts as a thin film. Ten dark fringes and nine bright fringes are observed from above the top plate. If the distance between the two plates along the separated edges is increased by 645 nm, how many dark fringes will there then be across the top plate? dark fringes will there then be across the top plate? Dark fingers

Explanation / Answer

By the condition

m = 2t

where t is the thickness of the air-film between the plates

Directly underneath the middle of a dark band), the edge of the plates (the edge where

they are not touching) are

t = 9/2 = 2909.5 nm apart

(where we have assumed that the middle of the 10th dark band is at the edge).

Increasing that to t' = 3547.5 nm

Would correspond to

m' = 2t'/ = 11

(since the first one corresponds to m = 0).

There are thus 12 dark fringes along the top plate.

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