3. [25 points]

    1. [15 pts] Below is shown a graph of intensity I versus angle q for a pattern produced on a distant screen by coherent light incident on three evenly spaced, very narrow slits.


      1. If the distance between adjacent slits is d = 4l , at what angle is point B? Show your work.

        2.  

        Point B is the third minimum, corresponding to a D Dadj of 4/3 l ,. Solving the equation dsinq =4/3l ,.for q gives 19.5° .

         

         

         

         

      2. For each of the following possible changes, state whether adjacent principal maxima would move farther apart, closer together, or remain at the same location as before. Explain your reasoning.

d sin q = nl , where n=0,1,2 etc. for the principal maxima. If d remains constant, sin q increase if the wavelength increases. Therefore, the angles to each of the principal maxima will increase and the adjacent principal maxima will move farther apart.

 

The location of the principal maxima does not depend on the width of the slit. The principal maxima will remain in the same location.

 

 

 

 

 
    2. [10 pts] One of the three slits is covered. It is observed that the intensity at point A increases. (See figure at top right of page.)

 

Was the change in intensity caused by covering slit 1, slit 2, or either slit 1 or 2? Explain your reasoning.

Since point A was originally a secondary maxima, D Dadj for each of the three slits is 1/2 wavelength. The path length difference for slits 1 and 3 is then a full wavelength. If slit two is covered, the light from slits 1 and 3 will interfere constructively, increasing the intensity at point A. If slit 1 is covered, the two sources would be out of phase at point A. Therefore, the intensity would increase at point A only if slit 2 were covered.