PHYS 275: Hw 2 Solutions
1-) Monochromatic light falling on two slits 0.042 mm apart produces the fifth-order fringe at a 7.8°
angle. What is the wavelength of the light used?
Solution:
.
2-) The third-order fringe of 650-nm light is observed at an angle of 15° when the light falls on two
narrow slits. How far apart are the slits?
Solution:
.
3-) A parallel beam of light from a He-Ne laser, with a wavelength 656 nm, falls on two very narrow slits
0.050 mm apart. How far apart are the fringes in the center of the pattern if the screen is 2.6 m away?
Solution:
(Note that for small angles, .
Now, since we also have
4-) In a water tank experiment, water waves are generated with their crests 2.5 cm apart and parallel.
They pass through two openings 5.0 cm apart in a long wooden board. If the end of the tank is 2.0 m
beyond the boards, where would you stand, relative to the “straight-through” direction, so that you
received little or no wave action?
Solution:
One would stand where there is no wave action meaning where there is destructive interference. Our task
then becomes one of finding x values (measured from the center of the screen) for the ava ilable minima.
The “availability” is stipulated by the sine function not exceeding 1. Thus we proceed as follows:
. Since L is to big compared with d and , angles involved are
small, thus , where x is where one should stand.
Obviously there will be as many x values as there are allowed m values. For clarity, let us Indicate all this
in a table:
