Two rectangular, optically flat glass plates (of index of refraction 1.37) are i
ID: 1655916 • Letter: T
Question
Two rectangular, optically flat glass plates (of index of refraction 1.37) are in contact along one end and are separated along the other end by a sheet of paper that is 58 mu m thick. The top plate is illuminated by monochromatic light (of wavelength 583 nm). An interference pattern results from the reflection of this light by the bottom surface of the top plate and the top surface of the bottom plate. What is the phase change as the light is reflected from the top surface of the bottom glass plate? Delta_Phi = 2 pi Delta_Phi = pi/2 Delta_Phi = 0 none of these Delta_Phi = pi Calculate the number of dark parallel bands crossing the top plate including the dark band at zero separation along the line of contact. The last dark band is to be counted if and only if its center (where the intensity is zero) is present.Explanation / Answer
Given two flat glass plates, n = 1.37
thickness of the sheet of paper, t = 50 micro meter = 58*10^-6 m
wavelength of light, lambda = 583 nm = 583*10^-9 m
a. When light is reflected off an interface where refractive index of the medium from where the light is coming is less than the refractive index of the medium on the other side of the interface, then that is called a hard boundary and causes a phase change of pi/2
Hence, phase change when the ray hits top surface of the bottom plate = pi/2 ( option 2)
b. consider at some point the seperation between the two plates (vertical) is h
then the path difference between the light ray reflected off the bottom surface of the top plate and top surface of the bottom plate is h
and, the opne of the ray is now phase shifted by 90 deg (pi/2), the one reflected off the bottom plate's top surface
so condition for destructive interference = h = n*lambda [ where n is a natural number ]
now, maximum h = t
so from n = 1 to n = n number of dark bands crossing the plate = t/lambda = 58*10^-6/583*10^-9 = 99.48
last band is lesser than half, so n = 99
adding the dark band at 0 seperation, n = 100 bands
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