Please refer to the uploaded image for the doubt

Asked by arjunsah797 | 14th May, 2022, 01:34: PM

Expert Answer:

Part (a) (i)
 
Path difference between A and D = d sinθ
 
Phase difference between A and D = ( 2π / λ ) ( d sinθ )
where d is distance between slits , λ is wave length of light.
 
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Part (a) (ii)
 
Path length ΔS between C and E,   ΔS = 2d sinθ
 
In order to get constructive interference between light rays emerging from C and A
 
ΔS = 2d sinθ = nλ
where n is an positive integer ( n>0 )
 
In order to get destructive interference between light rays emerging from C and A
 
ΔS = 2d sinθ = (2n+1) ( λ / 2 )
 
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Part (a) (iii )
 
For constructive interference, path length ΔS between light rays emerging from successive slits
 
ΔS = d sinθ = nλ
 
For second order diffraction n = 2
 
hence we get , 2 λ = d sinθ
 
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Part (b)
 
sine of angle of diffraction is given as
 
sinθ = n ( λ / d ) 
 
wavelength of light λ = 486 nm
 
distance between slits = 1/ N =  1 / ( 4.5 × 105 ) = 2.222 × 10-6
 
where N is number of lines per metre in the grating
 
sinθ = n ( λ / d ) = n ( 486 × 10-9 ) / ( 2.222 × 10-6 ) = 0.219 n
 
sinθ should be ≤ 1
 
Hence maximum value of n = 4
 
Maximum order of diffraction is 4
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Part (c)
 
whilte light consists of light rays of different wavelength ranging from 400 nm to 700 nm .
 
Hence different wavelengths have diffraction maxima at different angles.
 
In the diffraction pattern, we see maxima of different wavelengths at different points .
 
Hence we see rainbow of colors ranging from violet to red

Answered by Thiyagarajan K | 14th May, 2022, 04:40: PM