### Experiment 9

#### Refraction of Light (Snell's Law)

Objective:

The objective of this experiment is to verify the Snell's law of refraction by tracking a laser ray crossing the interface between two transparent media.

Equipment:

A computer with Internet connection, a calculator, a clear protractor, a few sheets of paper, and a pencil

Theory:

Refraction is the change in the direction of light as it changes medium.  The reason is the change in the speed of light.  The speed of light in vacuum is 300,000 km/s, in water 225,000 km/s, and in glass 200,000 km/s.  Different transparent media pose different light transmission properties.  It is the change in the speed of light that makes light bend as it enters a different medium.

A good analogy to this optical phenomenon is when a car enters a gravel road from a paved road.  If the gravel-asphalt borderline is straight and perpendicular () to the road edge as shown in Fig. 1, the car will continue straight but at a reduced speed due to more friction offered by gravel.   If the gravel-asphalt borderline is slanted as shown in Fig. 2, the car pulls to the side that offers more friction to the tire on that side.

 Figure 1: Front tires face equal frictional forces.  Car slows down but travels straight. Figure 2: Front tires face unequal frictional    forces.  Car slows down and pulls to the right.  One of the front tires is on gravel, the other still on asphalt.

Light behaves in a similar manner.  When a ray of light is incident perpendicularly on the interface between two transparent media, it enters the new medium without bending, but at a different speed as shown in Fig. 3.

When light crosses the interface of two media in a slanted way, bending (breaking) of light or refraction occurs. (Fig. 4.)

Fig.3                                            Fig. 4

In physics and engineering, normal line means perpendicular line.  For practical reasons, angles of incidence, i  and refraction, r are measured with respect to the normal line, N.  This is clearly shown in Fig.4.  Both i and r  are measured with respect to Line NN, called "normal to the interface."

Refraction Index

The refraction index n of a transparent medium is defined as the ratio of speed of light in vacuum to the speed of light in that medium.  The formula is

where c is the speed of light in vacuum (300,000 km/s) and v is the speed of light in the desired medium.  The refraction indices for water and glass are therefore,

Based on this definition, the refraction index of vacuum is 1 because

This is a constant by definition and may be used to any desired number of significant figures.

Air at normal atmospheric pressure is very dilute and has a refraction index of 1.00 very close to that of vacuum.

nair = 1.00

Snell's Law of Refraction:

The Snell's law simply relates angles i and r to the refraction indices of the two media n1 and n2 .  It is easy to show that

n1 sin i  = n2 sin r

Example: A light ray that makes a 42.0o angle with water surface enters water from air.  Find its angle of refraction It means the angle it makes with the normal line in water.  Also find the deviation angle D.

 Solution: n1 = 1.00, n2 = 1.33,  i = 90.0o - 42.0o = 48.0o ,      r = ? Using Snell's law results in:    n1 sin i  = n2 sin r. 1.00 sin (48.0o)  = 1.33 sin(r)  sin(r) = sin (48.0o) /1.33 ;    r = 34.0o.   D =  i - r  =  48.0 - 34.0  = 14.0o.

Procedure:

If you have not done so, you may need to add the following Website to your Java exception list: http://www.walter-fendt.de/.   To do this, follow the path (Windows operating system),

Start → All Programs → Java → Configure Java → Security (use High) → Edit Site List … → Add → Type in the site URL (http://www.walter-fendt.de/).

Click on the following applet:  http://www.walter-fendt.de/ph14e/refraction.htm .  The applet shows a ray of light (Laser-like) coming from the top left corner.  At the point of incidence on the interface it is partially reflected and partially refracted.  Both the top medium and the bottom medium can be selected from the dropdown windows.  The angles of incidence (black), reflection (blue), and refraction (red) are determined by their colors.  Holding the top left of the incident ray with the mouse, it allows you to move it and change the angle of incidence.  As you change the angle of incidence, the angles of reflection and refraction change as well and their values appear on the right in respective colors.  You are expected to calculate these angles, and record the results to 5 decimal places in Table 1 below.

Part 1:  Air-Water Interface

Select air (n1 = 1.00) as Medium 1, and water ( n2 = 1.33) as Medium 2.    Set the angle of incidence at 15o with respect to the normal line by holding the mouse on the incident ray.  Measure it with a protractor and see if it is correct.   Measure the angles of reflection and refraction (also with respect to the normal line) with the protractor and record all angles in Table 1.  These must be recorded under the measured values.

The accepted value for the angle of reflection is of course, the same, 15o.    Calculate the accepted value for the angle of refraction from the Snell's formula and record the result in Table 1 (5 decimal places).

Repeat the above steps for angles of incidence 30o, 45o, 60o, and 90o.  Each time the angle of refraction must be recorded to 5 decimal places.

Part 2:  Air-(Flint Glass SF2) Interface

Select air (n1 = 1.00) as Medium 1, and flint glass SF2 ( n2 = 1.65) as Medium 2.  Follow the exact procedure as in Part 1.

Part 3:  Benzol-Water Interface

Select Benzol (n1 = 1.50) as Medium 1, and water ( n2 = 1.33) as Medium 2.   Note: This time n2 < n1 .

Follow the exact procedure as in Part 1 and also determine the maximum angle of incidence for which refraction still occurs.  Record that angle in Table 1.  Make an explanation to this effect in your conclusion.

Data:

Given and Measured:

 Trial Measured Accepted (Calculated) % Error Incidence Angle (o) Reflection Angle (o) Refraction Angle (o) Reflection Angle (o) Refraction Angle (o) Part 1 Air-Water Interface ///////// 1 15o 2 30o 3 45o 4 60o 5 90o Part 2 Air-(Flint Glass SF2) Interface ///////// 1 15o 2 30o 3 45o 4 60o 5 90o Part 3 Benzol-Water Interface ///////// 1 15o 2 30o 3 45o 4 60o 5 (    o)

Calculations:  Apply the Snell's formula to find the accepted values for angles of refraction (5 decimal places), in each case.

Comparison of the Results: Calculate a % error on the angle of refraction in each trial.

Conclusion: To be explained by students

Discussion:  To be explained by students