### Experiment 6

#### 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 passing through a rectangular slab of glass.

Equipment:

A rectangular slab of glass, a laser pointer, a few sheets of paper, a sharp pencil, a ruler, and a protractor

Theory:

Refraction is the abrupt change in the direction of light as it suddenly changes medium.  The reason is the change in speed of light in different media.  The speed of light in vacuum is 300,000 km/s, in water 225,000 km/s, and in clear glass 200,000 km/s.  Different transparent media pose different light transmission properties.

A good analogy to this optical phenomenon is when a car enters a gravel road from asphalt.  If the gravel-asphalt borderline is straight and perpendicular () to the road's edge as shown in Fig. 1, the car will continue straight but at a reduced speed due to increased 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 and changes direction.

 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.

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. Fig. 3.

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

Fig.3                                            Fig. 4

In physics, math, 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 NN or normal line to the interface at the point of incidence.

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 = 300,000 km/s is the speed of light in vacuum and v is the speed of light in the subject medium.  The refraction indices for water and glass are therefore,

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

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

n air = 1.00

Snell's Law of Refraction:

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

n1 sin i  = n2 sin r

Example:  A ray of light that is making a 42.0 o angle with water surface enters water from air.  Find the refraction angle as well as the deviation angle D.

 Solution: n1 = 1.00, n2 = 1.33,  i  = 90.0o - 42.0o  =  48.0o   Using n1 sin i  = n2 sin r, we get: 1.00 sin48.0o = 1.33sin r  ;   sin r = sin 48.0o/1.33  ;   r = 34.0o D = i - r = 48.0o - 34.0o = 14.0o. Figure 5

Procedure:

1. Place a flat sheet of paper on a flat surface.

1. Place or mount the laser pointer such that its ray is not only horizontal to the sheet of paper, but also travels very close to its surface and leaves a streak (line) of red light on the paper.  Some adjustment and practice is crucial.

1. When an uninterrupted streak of light is present, place the rectangular or square slab of glass on the flat paper such that the laser ray is incident on a clear side of it (as shown in the figure) and exits from the opposite side.  With a sharp pencil, draw four straight lines around the slab in order to register the contour of the slab on the paperAlso, place two dots on the incoming ray and two dots on the exit ray.

The ray incident on side AA of the slab making angle i1 with N does refract and enters the slab through angle r1.   See Fig. 6.  In glass, it travels to the opposite side BB and becomes incident on it through angle i2 and finally refracts back into air through angle r2.

Figure 6

1. Lift the slab and turn the laser off.  On the paper, connect the marked points in order to draw the trace of the ray.

1. Draw two N (Normal) lines as shown in Fig. 6.  Measure angles i1 , r1 , i2 , and r2 by a protractor.

1. Use i1 and r1 and the Snell's formula to find n, the refraction index of the slab (glass).  Use i2 and r2 to find n again.  Find the average of the two values of n.  Use this average as your measured value of n.

1. Calculate a percent error using the accepted value of naccptd = 1.50 for regular clear glass.

Data:

Given:        naccptd = 1.50  (for regular clear glass)

Measured:  Angles i1 , r1 , i2 , and r2

Calculations:  Apply the Snell's formula to find n once by i1and r1, and once by i2 and r2.

Comparison of the Results: Calculate a % error on n using the usual %error formula.

Conclusion: To be explained by students.

Discussion:  To be explained by students.