Refraction and reflection of light

When a ray of light impinges on a surface where two different materials meet, part of the ray is reflected and part of it is transmitted. If the ray is perpendicular to the surface, then the incident ray, the reflected ray and the transmitted (refracted) ray all lie along the same line (i.e they are collinear). If the ray is not perpendicular to the surface, then the ray appears to be bent at the surface. The amount of bending depends on how close the ray is to being perpendicular and on the properties of the two surfaces.

To measure how close the ray is to being perpendicular, we measure the angle between the incident ray and the normal (a line perpendicular to the surface) that meets the surface at the same point the ray does. This angle is called the angle of incidence. Depending on the situation the refracted ray may bend toward or away from the normal. To determine this bending, we measure the angle between the refracted ray and the normal. This angle is known as the angle of refraction.

The property of the materials that is important in determining the amount of bending is the speed of light in the material. The speed of light in a material v is related to the speed of light in a vacuum (which is denoted c) through the material's index of refraction n.

Since the speed of light in the material cannot exceed the speed of light in the vacuum, n must be greater than one. Actually what is important in determining the amount of bending of rays is the ratio of the speeds.

All of these results are combined into Snell's law.

In our case, one of the media will be air, and the index of refraction of air is very close to one.

Part I.

1. Place a quadrilateral prism from the optics kit on a sheet of paper on top of the corkboard.
2. Have a light source shine on it.
3. Note the point where the light enters the prism (let's call it O) and some point along the light's path to the prism (let's call it P₁). Mark it with a pen or pencil, you will be turning in these sheets along with your lab writeup.
4. Also note the point on the opposite side where the light leaves the prism (let's call it Q₁); it must be marked at the surface. (Note that in Part I the surface we are interested in is the first surface, where the medium changes from air to plastic.)
   
   
   
   
   
   
5. One must construct a normal at the point O.  If the subsequent beams (other incident angles) one collects have the same O then one has fewer normals to construct; however, it is not necessary for the beams to have the same origin.  Make four sets of measurements altogether (P₁ – P₄ and Q₁ – Q₄). You should have as wide a range of angles as possible, though you should avoid very small angles since they are difficult to measure.
6. Draw a line representing the prism's surface where the light entered and a normal to that line through the point of entry O. (Do not draw a line you "think" is perpendicular but use some method to make sure the line is as close to perpendicular as you can make it; you will lose points for a bad normal line.)
7. Draw lines from your P's to O (or O's) and from your Q's to O (or O's) and measure the incident angles θ_i (between OP_n and the normal) as well as the refractive angles θ_r (between OQ_n and the normal).
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
8. You must submit this sheet as part of the lab report. If the angle between the normal and the surface is not within 3 degrees of a right triangle you may lose points. If any measured angle is off by more 3 degrees you may lose points.
9. According to Snell's law for this case, sin θ_i = n sin θ_r, where n is the index of refraction. Plot sin θ_r vs. sin θ_i and extract n. (If you use Excel to calculate the sine of the angles remember that Excel uses radians and that there is a function for converting degrees to radians.)

Part II.

Repeat the measurements above for the square shaped objects made of different material. You might want to stack two of them together so you are not confused by the light which simply passes over the block.

Part III.

1. Note that in this part we will focus our attention on the second surface. Place the quadrilateral prism used in Part I with the slanted end away from the light source (i.e. the two right angles should be closest to the light source).
   
   
   
   
   
   
2. The light may or may not pass through the opposite face. Starting from an angle where light passes through, slowly change the angle and find the first angle at which no light passes through.
3. Mark the point A at which the light enters the prism and the point B from which it reflects on the opposite side.
4. Draw the interface of this slanted side and construct its normal through point B. (Note that for this measurement we are interested in the second surface, where the medium changes from plastic to air.)
5. The angle between AB and the normal is called the critical angle θ_c. It can be related to the index of refraction. How? Obtain n and compare this measurement of n to that of Part I.
6. Dispersion occurs when the speed of light is different for different frequencies. You should notice some dispersion close to the critical angle. Observe this effect and use it to determine whether the speed of red light is faster or slower than the speed of blue light in this particular material. Don't just state an answer, but give the details of your reasoning based on your observations. Your reasoning should be based solely on your observations, Snell's law, and the meaning of n, the index of refraction. (That is, you should include nothing about frequency or wavelength.)

Part IV.

1. Again in this part we are focusing on the second surface. In the arrangement described above, for angles both slightly less and slightly more than θ_c, you should observe a reflected ray from the surface.
2. For two incident angles less than θ_c and two greater than, measure the corresponding angle of reflection (the angle between the normal and the reflected ray of light).
   
   

   Angle of incidence	Angle of reflection

   
   
   
3. How are the angles of incidence and reflection related?
4. What do you observe about the intensity of the reflected ray as the angle of incidence passes through the critical angle?