All GRE Subject Test: Physics Resources
Example Question #3 : Electromagnetics, Waves, And Optics
A double slit experiment is set up with the following parameters: two slits are a separated by a distance . A beam of light with wavelength shines through the two slits, and is projected onto a screen a distance from the slits. What is the distance on the screen between the central band and the next band on either side? (This distance is marked '' on the figure).
The condition for constructive interference with double slit diffraction is given by:
Where is 0, 1, 2, ...
Solving for the angle and using the small angle approximation, we get;
The distance in the diagram can be related to the other quantities by simple geometry:
Again, with the help of the small angle approximation. Setting the two thetas equal to each other and solving for , we get:
For the central band, , so the position is also zero. The next band, , yields a distance of:
Example Question #4 : Electromagnetics, Waves, And Optics
Two waves with frequencies: are combined. What is the frequency of the resulting beat?
The beat from two combined sound waves is: