InterviewSolution
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InterviewSolution
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Monochromatic light of wavelength `5000 Å` is used in YDSE, with slit width, `d = 1 mm`, distance between screen and slits, `D = 1 M`. If intensites at the two slits are `I_1 = 4I_0 and I_2 = I_0`, find: a. finge width `beta:` b. distance of 5th minima from the central maxima on the screen, c. intensity at `y = (1)/(3) mm,` d. distance of the 1000th maxima, and e. distance of the 5000th maxima. |
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Answer» (i) `beta=(lambdaD)/(d) =(5000xx10^(-10)xx1)/(1xx10^(-3))=0.5 mm` (ii) `y=(2n-1) (lambdaD)/(2d),n=5 rArr y=2.25 mm` (iii) At `y=(1)/(3) mm, y lt lt D` Hence `Deltap=(dy)/(D)` `Delta phi=(2pi)/(lambda)Deltap=2pi (dy)/(lambdaD)=(4pi)/(3)` Now resultant intensity `I= I_(1)+I_(2) sqrt(I_(1)I_(2)) cos Delta phi =4I_(0)+I_(0)+2 sqrt(4I_(0)^(2)) cos Delta phi =5I_(0)+4I_(0) cos (4pi)/(3) =3I_(0)` (iv) `(d)/(lambda)=(10^(-3))/(0.5xx10^(-6))=2000` `n=1000` is not ` lt lt 2000` Hence now `Deltap=d sin theta` must be used Hence, `d sin theta =nlambda=1000lambda` `rArr sin theta=1000(lambda)/(d)=(1)/(2) rArr theta =30^(@)` `y=D tan theta=(1)/(sqrt3)` meter (v) Higest order maxima `n_(max)=[(d)/(lambda)]=2000` Hence, `n=5000` is not possible. |
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