Light of wavelength 575 nm falls on a slit 0.0516 mm wide. (a) On a very large d

Question

Light of wavelength 575 nm falls on a slit 0.0516 mm wide.

(a) On a very large distant screen, how many totally dark fringes (indicating complete cancellation) will there be, including both sides of the central bright spot? Solve this problem without calculating all the angles! (Hint: What is the largest that sin can be? What does this tell you is the largest that m can be?)     (dark fringes)

(b) At what angle will the dark fringe that is most distant from the central bright fringe occur?     (degrees)

Explanation / Answer

a) dark spots appear in a single slit diffraction when the path difference of two waves differ by , 2,3,... or

= n where n=1,2,3,4... or by the following equation:

asin = n

=575nm= 5.755E-4 mm
a=0.0516mm

max dark fringes on a flat screen occur when =90°, so:

0.0516sin(90°) = (5.75E-4)n
n= 89.74 but we round off to n=89. which means that there are 89 dark fringes on both sides and the total is 89+89=178 dark fringes.

b) the farthest dark fringe that will appear is at n=89.

0.0516sin = 89(5.75E-4)
sin 0.99176
=84.2°

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