problem 1: Laser beam with wavelength 632.8 nm is aimed perpendicularly at opaqu

Question

problem 1: Laser beam with wavelength 632.8 nm is aimed perpendicularly at opaque screen with two identical slits on it, positioned horizontally, and close enough to each other so that both of them fall in the beam. A precise positioning shield is used to cover alternatively one of the slits, while the other remains open. On an observation screen positioned 1 meter further from the opaque screen, the diffraction patterns from the independent slit illumination were found identical, with minima 4.0 mm apart. The interference pattern maxima from simultaneous illumination of both slits (shield removed) were 1.0 mm apart. What are the double slit characteristics (slit width, slit separation)? Provide the result in millimeters.

i found that the answers for part 1: slit width= 0.158 mm slit separation= 0.633 mm

problem 2: On the setup described in problem 1, the opaque screen with slits was replaced with a diffraction grating with 20 slits/mm. What distance between the diffraction maxima is to be expected on the observation screen?

Explanation / Answer

1) for width: y = lambda L/a

a = lambda L/y = 632.8E-9*1/4.0E-3=0.158 mm

for seperation

d = lambda L/y = 632.8E-9*1/1.0E-3 = 0.633 mm

2) now y = lambda L/d

but d = 1/20 mm = 0.05E-3

so y = 632.8E-9*1/0.05E-3=0.0127 m = 12.7 mm

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