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Asked by vishakhachandan026 | 10 Apr, 2019, 09:30: AM
answered-by-expert Expert Answer
A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of incident beam. At first minimum of diffraction pattern, the phase difference between rays coming from edges of slit is, 
 
We know, the phase difference between the top and bottom rays of slit width 'd' is Φ.
 
ϕ space equals space fraction numerator 2 pi d over denominator lambda end fraction sin theta
The angular position of nth secondary minima is,
 
 sin theta almost equal to theta almost equal to space fraction numerator n lambda over denominator d end fraction
So, the first minima will occur at, 
 
sinθ = λ/d
 
Thus,
 
ϕ equals space fraction numerator 2 pi d over denominator lambda end fraction open parentheses lambda over d close parentheses space equals space 2 pi ... option (d) 
 
The angular position of nth secondary maxima is 
 
sin theta almost equal to theta almost equal to space fraction numerator left parenthesis 2 n plus 1 right parenthesis lambda over denominator 2 d end fraction T h u s comma space a n g u l a r space p o s i t i o n space o f space f i r s t space s e c o n d a r y space m a x i m a space w i l l space b e space sin theta space equals space fraction numerator 3 lambda over denominator d end fraction T h u s comma space space ϕ space equals space fraction numerator 2 pi d over denominator lambda end fraction open parentheses fraction numerator 3 lambda over denominator 2 d end fraction close parentheses space equals space 3 pi
 
Answered by Shiwani Sawant | 10 Apr, 2019, 12:27: PM
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