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Design a double slit system (i.e find a:d) ratio in which the fourth fringe not counting the central maxima is missing.

Design a double slit system (i.e find a:d) ratio in which the fourth fringe not counting the central maxima is missing.

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Grade:12th pass

2 Answers

Harshit Singh
askIITians Faculty 5965 Points
11 months ago
Dear Student

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kindly provide complete and clear question
Thanks
Siddharth Jawa
15 Points
11 months ago
dsinθ = mλ (for bright fringe)
sinθ = mλ/d    
I = Io(Sinβ/β)^2    where, β=α/2= 2pi x δ/2λ
β = pi *delta / lamda       (delta= Asinθ)
β = pi *asinθ / lamda      (sinθ= m*lamda/d)
β = pi *a*m*lamda / d*lamda  = pi*a*m / d  (m=4)
β = 4*pi*a / d 
( for intensity = 0 at m=4, β should be an integral multiple of pi)
where, 
d= separation of slits ; a= slit width 
Therefore, 
pi= 4*pi*a/d
d=4a
a/d= 1/4
which implies 
a:d = 1:4
 

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