more Snell's Law

Snell's Law.

Look at the diagram above. We have 6 interfaces where the ray of light will go from one material to another. The water tank is made from glass with an index of 1.523, the water has an index of 1.33, and the monolith in the center is of some mythical hi-index glass with an index of 1.75. Lets follow the ray of light through the tank from the light to the eye.

  1. First the ray goes from air into the glass of the tank. If the angle of incidence is 35 degrees, what is the angle of refraction?

    2.  
  2. Second, the ray goes from the glass into the water. If the angle of incidence is 22 degrees, what is the angle of refraction?

    3.  
  3. Third the ray travels from the water into the hi-index glass. Suppose I can somehow determine that the angle of refraction is 22 degrees. Then what was the angle of incidence?

    4.  
  4. OK, to leave the monolith the ray is at 0 degrees to the normal -- it is perpendicular to the side. What is the angle of refraction?

    5.  
  5. This side of the tank was made of something else, not the same glass as the rest of the tank, and I do not know what it's index is. But I manage to determine that the angle of incidence is 12 degrees; then I determine that the angle of refraction is 10 degrees. What is the index of refraction of the new material?

    6.  
  6. Last, the ray leaves the tank altogether. The angle of incidence is 10 degrees. You found an index in the last problem. So, what is the angle of refraction?

    7.  
OK. Well. What do we do now? We take the problems one at a time, and do each one a step at a time!

First get out some paper, and follow the rules below for the first interface, where the ray enters the tank. Write out the formula and the list of variables each time. Then you do the second one . . . after a few of them, click here to see how you are doing. Then come back, and do a few more. Write out the formula and the variable list for each one of the problems.


SNELL'S LAW

  1. Read the problem through, and identify it as a Snell's law problem. 

    2. Write out the formula, then the list of variables.
           () (sin i) = () (sin r)
    =
    <i =          sin i =
    = 
    <r =          sin r =
     
  2. Read the problem phrase by phrase, and fill in the list of variables. Make sure that the side the ray is coming from is the incident or 'i' side, and the side the ray is going to is the refracting or 'r' side.

    3.  
  3. Substitute the numbers for the variables in the equation.

    4.  
  4. Solve the equation for what is not known. If an angle is not known, you are trying to get the whole term 'sin i' or 'sin r' on one side of the equation; then you punch '2nd' sin to get the angle. If both angles are known, you will substitute their sine's in the equation, so you will not do '2nd' sin.

Go back to the Snell's law page.
 


copyright Ellen Stoner, 1998