wave-optics Question 19

Question: Q. 10. Yellow light (λ=6000\AA) illuminates a single slit of width 1×104 m. Calculate : (i) the distance between the two dark lines on either side of the

central maxima, when the diffraction pattern is viewed on a screen kept 1.5 m away from the slit, (ii) the angular spread of the first diffraction minima.

A [O.D. Comptt. I, II, III 2012]

Show Answer

Solution:

Ans. Separation between two dark bands on each side of central bright fringe = width of bright fringe ,

We know width of the central fringe

=2Dλa

where,

D= distance of slit from screen,

λ= wavelength of the light,

a= width of the slit. 1/2

According to question,

Width of central fringe =1.5×2×6000×10101×104 m

So the distance between the two dark lines on either side of the central maxima

Angular spread of the first diffraction minima

=λa =6000×1010 m1×104 m =6×103rad



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