Question

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.

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?

Answer 1

Part A)
For the single slit, apply

y/L = m(wavelength)/a

.004/1 = 1(632.8 X 10^-8)/a

a = 1.58 X 10^-4 m

That is 0.158 mm

For the double slit, apply

y/L = m(wavelength)/d

.001/1 = 1(632.8 X 10^-9)/d

d = 6.328 X 10^-4 m

That is 0.6328 mm

Thus slith width is .158 mm and slit separation is .6328 mm

Part B)
For a diffraction grating, apply

y/L = mwavelength)/d

d is the inverse of the slits per mm, converted to meters

d = 1/20000

y/1 = 1(632.8 X 10^-9)/(1/20000)

y = .0127 m

That is 1.27 cm or 12.7 mm