Question

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?

Answer 1

Answer:

1 slit width = 0.158 mm slit separation = 0.633mm 2. distance between diffraction maxima = 12.7mm

Explanation:

Define the terms

λ, wavelength of beam

D, Distance from plane to slit

x, Distance between diffraction pattern minima (for single slit experiment)

w, fringe width (for double slit experiment)

1. For double slit experiment fringe width is also known as distance between Maxima

w=λD/d, which rearranging for d=λD/w

d= (632.8 x 10^-9 x 1 x 10^3)/1

d= 0.633mm

For single slit diffraction, minima is located at angles given by a.sinΘ= m.x

where a is the slit width and m is an integer

For small angles

Θ= (x/D) = (λ/a)

a= λD/a

a= (632.8x10^-9 x 1)/4

a= 0.158mm

2. Grating has 20slits/mm, hence, d= 1/20mm= 0.05x10^-3

y(distance between successive maxima)= λL/d

y= (632.8 x 10^-9 x 1)/0.05x10^-3

y= 12.7mm