In the figure shown three slits s 1 , s 2 and s 3 are illuminated with light of wavelength λ . λ << d and D >> d. Each slit produces same intensity Ι on the screen. If resultant intensity at the point on screen directly infront of s 2 is 3 Ι then the maximum value of λ is 
(i) Find value of n.
(ii) Also find intensity at point P if λ is of part (i)
Text Solution
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(i) 3 (ii) 3 Ι
Sol. (i) 
Q is equidistant from s 1 and s 3
Resultant amplitude due to light coming from S 1 and S 3 is
A R = 2A
Resultatnt amplitude at Q
A R = 
= (2A) 2 + A 2 + 2 2A × A cos φ
3A 2 = 5A 2 + 4A 2 cos φ
– 
= cos φ , φ = 
, 
Δ x = 
– D
= D 
= 
× 
= 
for λ max
λ = 
(ii) 
Intensity for point 'P'
Δφ for S 1 and S 2 at P = 
Δφ for S 1 and S 3 at P = 
∴ Again Area = 
= 
∴ I P = 3I
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