In the figure, a broad beam of light of wavelength 638 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 17.3 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? Incident light (a) Number Units (b) Number Units >
In the figure, a broad beam of light of wavelength 638 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 17.3 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? Incident light (a) Number Units (b) Number Units >
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Transcribed Image Text:In the figure, a broad beam of light of wavelength 638 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 17.3 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?
Incident light
(a) Number
i
Units
(b) Number
i
Units
Expert Solution
Concept and Principle:
The bright and dark pattern is created when two waves interfere with each other this is called interference of light. The spacing between the plates can be calculated from the wavelength.
First, consider bright spot at the end,
For the next dark spot,
Now the rate of change will be given by,
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