(a) If one of two identical slits producing interference in Young's experiment is covered with glass, so that the light intensity passing through it is reduced to 50%, find the ratio of the maximum and minimum intensity of the fringe in the interference pattern. (b) What king of fringes do you expect to observe if white light is used instead of monochromatic light?

MY DOUBT IS: In the first part of the question, shouldn't there be no interference pattern formed as introducing a glass sheet will make the slits non-coherent?

Asked by rayyan20151 | 19th Jan, 2020, 09:18: PM

Expert Answer:

Figure shows the arrangement so that glass of thickness t is introduced before a slit S2 to reduce the intensity
of light from S2 as 50% of that of light from S1 .
 
To get constructive interference at P on screen , we need to find the path difference of two light beams
from source S by including the additional optical path introduced by glass.
 
Path difference Δd = [ SS1 + S1P + SS2 + (μ-1)t + S2P ]
 
where μ is the refractive index of glass and t is thickness of glass.
 
If Δd = nλ , then we get maximum intensity due to constructive interference , where n is integer and λ is wavelength.
 
Similarly if pathdifference satisfies destructive interference, we get minimum intensity at P.
 
Hence even after introduction of glass plate to reduce the intensity of light, we get interference pattern on screen
 
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Intensity I = I1 + I2 + 2 (I1I2)1/2 cosδ
 
where δ is phase difference
 
Let I1 = Io  and I2 = ( Io / 2 )  
 
For maximum, we have δ = 0 , Hence  begin mathsize 14px style I subscript m a x end subscript equals space left curly bracket space square root of I subscript o end root space plus space square root of 0.5 space I subscript o subscript space end subscript end root space right parenthesis squared space equals 2.9 space I subscript o space end subscript end style
For minimum, we have δ = π , Hence  begin mathsize 14px style I subscript m i n end subscript equals space left curly bracket space square root of I subscript o end root space minus space square root of 0.5 space I subscript o subscript space end subscript end root space right parenthesis squared space equals 0.086 space I subscript o space end subscript end style

Answered by Thiyagarajan K | 20th Jan, 2020, 08:41: AM

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