Please refer to the uploaded image for the doubt

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