In class we have identified three different models to describe light:  the ray model, the wave model, and the photon model.  How do we know when to use one rather than another?  In this recitation we explore the circumstances under which we can safely ignore the wave properties of light and treat light as a ray, and the circumstances under which we run into trouble by doing this,  Later in the course we will explore the circumstances for which a photon model is useful.

The ray model, in which we imagine light as a straight line traveling in a particular direction, works quite well when examining the interaction of light with lenses and mirrors.  Why are we allowed to ignore the wave-like aspects of light in these circumstances?  Why do we not see interference patterns everywhere all the time?

1) Since light is a wave, what is really being represented by the ray in a ray diagram?  Create a representation of light that shows both the wavefronts and the rays.  (Hint: Consider the water waves from the reading.)  How would your drawing change if the wavelength changed?

2) Now imagine that your wave of light encounters a small slit.  What happens to the wave as it passes through the slit?  Recall that each point on the wave front acts as its own point source, so there are multiple point sources contained inside the slit width.   Draw what happens (consider using the back of the page for this, it's easier if you draw it BIG!):

3)  Now suppose that we put a screen far past the slit.  What would we see on the screen?  (Hint: Recall Thomas Young's experiment.)

4) Now consider what would happen if you made your slit much much larger, but keep the wavelength the same.  What would we see on the screen then?

Let's now try to understand the difference between the two scenarios we have just described (the small slit and the large slit) a little more quantitatively.  Recall that each point on the incoming wavefront can be considered a point source, and that light coming from different point sources can interfere either constructively or destructively at various points on the screen.

5)  Consider the wavefronts emerging from two point sources, one at the top of the slit and one in the middle of the slit.  What is the difference in pathlength traveled by the two wavefronts between the slit of width a and point P on the screen? 

6)  When will you get destructive interference for the waves? Convince yourself that destructive interference (dark spots) will occur at the screen for values of theta satisfying a*sin(theta) = m*lambda, where lambda is the wavelength of the incoming light.  Note that this is not quite the same as the double-slit result! 

7)  Consider only the first dark spots to the left and right of the central maximum, i.e., the m = 1 dark spots.  Where will these m = 1 dark spots occur in the case of lambda << a (the large slit case)?  What happens in the case of lambda > a (the small slit case)?  What happens when lambda < a but not by much, i.e., the intermediate case?  For each case, draw what you will observe on the screen.

8) What does your answer to the previous question tell you about the conditions under which interference effects are important to consider, and when they can be safely neglected?  Does this answer the question posed at the beginning of the recitation about why it's ok to treat light as a ray (suppressing the wavelike properties of light) when thinking about lens and mirror problems? 

BONUS!!  The work you have done here suggests that when the size of a slit is on the same order of magnitude as the wavelength of light, interference effects will be important to consider.  Such interference effects are used in the imaging technique known as "crystallography" in order to determine the structure of biological molecules like proteins.  What wavelength of light would you want to use in crystallography?  Why?

BONUS x 2!!  Why can we hear around corners but not see around them?