Single slit diffraction quesitons H/w problems A single slit of width 0.300 mm i

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Single slit diffraction quesitons

H/w problems A single slit of width 0.300 mm is illuminated by 535 nn laser Iwhat color is this? How far from each other on the sereen 2 m behind are the m and m- 1 minima of diffraction? 2 and m n 0 and n maxima (that is, the cen 1ra maximum and the first side maximum and n 2 maxima? How many maxima are there on the screen overall? 2) Can Hubble telescope (mi mor of diameter D 3.00 m) see a person on the Moon (assume that a person is abou 70 m tall and that "to see" a person means barely resolve two objects al 7 m distance apart) Exactly how close two objects can be on the Moon to be sorn by the Hubble telescope? Distance to the Moon is about 380,000 km. 3) A dinraction grating with 500 linesmm is illuminated by the blueviolet laser poin ength), How far from each other are the and n dimraction spots on the wall which is 1.00 m behind the grating? n 1 and n 2 spots? How many spots are there on the Why not more?

Explanation / Answer

i. 535 nm stands for green light.

ii. for minima,

y = (m -0.5) lambda D/ d

y_+1 = 0.5 x 535 x 10^-9 / (0.3 x10^-3)

= 8.92 x 10^-4 m

y_-1 = - 8.92 x 10^-4 m

distance between them = 1.78 x 10^-3 m

iii. for minima,

y = (m -0.5) lambda D/ d

y_+1 = 1.5 x 535 x 10^-9 / (0.3 x10^-3)

= 2.675 x 10^-3 m

y_-1 = - 2.675 x 10^-3m

distance between them = 5.35 x 10^-3 m

iv for maximum

y = m * lambda * D / d

distance = 1 x 535 x 10^-9 / (0.3 x 10^-3) = 1.78 x 10^-3 m

v. distance = (2 - 1) x 535 x 10^-9 / (0.3 x 10^-3) = 1.78 x 10^-3 m

vi. sin(theta) = m lambda / d

sin90 = m (535 x 10^-9) / (0.3 x 10^-3)

m = 560.75

hence there will be 560 maxima.

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