Index of Refraction
Abstract Refraction is change in direction that occurs when a wave encounters the interface between two media. Together, refraction and reflection account for the basic principles behind nearly all optical devices. Snell discovered the equation for refraction,
through experiments with light rays, long before light was proven to be a wave. Snell's law can be proven based on the geometrical behavior of waves. Here n is the index of refraction. Snell invented this quantity to describe the refractive properties of various substances, but it was later found to be related to the speed of light in the substance,
where c is the speed of light in a vacuum. In general a material's index of refraction is different for different wavelengths of light.
I. Introduction How light moves through space has been a question in physics for hundreds of years. In this lab exercise, light can be approximated as travelling in straight lines, or rays, from a light source. In moving through space, these light rays can interact with matter in two ways, through reflection and refraction. If a light ray shines on a smooth flat surface, then at least part of the ray will “bounce off” of the surface, or be reflected. If the angle of incidence, θincident, is measured with respect to a line perpendicular to the surface (known as the normal), then the angle of incidence is equal to the reflected angle.
(1)
If light shines on a transparent material, then part of the light ray will pass through the material. The part of the ray that passes into the material is “bent” or refracted. This bending, or change in the direction of the ray occurs only at the interface between the two materials. The interaction of the light with the transparent material changes the speed of light as it passes through the material. The relationship between the speed of light in a vacuum c and the speed of light in the material v is known as the index of refraction n. The index of refraction is defined in the following equation: n=cv (2) This speed change causes the light ray to bend. Equation 2 can be used to find a relationship between the angle of the incident wave, still measured with respect to the normal, and the angle of the light ray as it moves through this second material, known as the angle of refraction. This new relationship is known as Snell’s Law, stated mathematically in the following equation: (3)
In this equation, moving through,
is the index of refraction of the medium the incident ray is is the incident angle, nr is the index of refraction of the
medium the refracted ray is moving through, and
is the angle of refraction.
In Figure 2, it has been assumed that nr is larger than
so that the refracted
ray is deflected toward the normal. If the incident medium has the larger index of refraction, then the refracted ray will be deflected away from the normal. In this case, if the angle of incidence is large enough, the refracted ray will be bent through an angle equal to, or larger than, 90◦ so that the ray will remain inside the material. This is known as total internal reflection, and is the basis for fiber optics used in telecommunications. Using Snell’s law, the minimum, or critical, angle for total internal reflection can be found by setting the refracted angle,
in Equation 3, to 90◦ so that the
sin(90◦ ) is one. Substituting this into the Equation 3, we get the following: (4)
In this equation,
is the index of refraction of the incident medium,
index of refraction of the refraction medium, and
is the
is the critical angle for total
internal reflection.
II. Methodology Materials and Apparatus:
Cardboard Light source with single slit Ruler and protractor Graphing papers for cardboard Masking tape and pins Plastic cuvette Specimens o Semicircular plastic lens o Water
Procedures: 1. Tape a sheet of graphing paper on the cardboard. Draw a horizontal line and a vertical line intersecting at the middle of the graphing paper. The horizontal line serves as the boundary between the two media while the vertical line is the normal line. On either sides of the normal or 0° line, mark off the angles 8°, 16°, 24°, 32° and 40° using a protractor. 2. Place the semicircular lens on the graphing paper such that the midpoint of the flat surface of the lens coincides with the point of intersection in the graphing paper. Switch on the light source. By sliding the piece of plastic found on the rear part of the casing of the light source slowly and carefully, the width of the beam of the light coming out of a slit can be controlled so that a light ray (approximating a thin line) is obtained. 3. Position of the light ray (or the slit) near the lens and along the 0° line, this line lies normal or perpendicular to the flat surface of the lens
which serves as the interface between the lens material and the air. Note that the light ray passes through the lens and goes out into the air without being refracted. 4. Stick a pin into the graphing paper and cardboard at the midpoint of the flat surface of the lens. This is the point where the light beam should come out of the first medium. 5. Position the slit of the light source such that the incident light ray lies along an angle of 8° from the normal line. The distance between the slit and the curved surface of the lens should be small. This angle of 8° is the angle of incidence . Record this angle in the worksheet. 6. Observe the light ray which comes out of the flat surface of the lens. This is the refracted ray. Make sure that this refracted ray comes out of the lens. Stick a second pin to the graphing paper at a point along the path of this refracted beam, about 2cm from point A (where the first pin is). Label this second point as B. The angle defined by the normal line through point A and the line drawn from point A to point B is the angle of refraction 7. Position the slit of the light source next, at an angle of 16° from the normal line. Repeat steps 5 and 6. Do this also for angles of 24°, 32° and 40°. Each time, record the corresponding value of the angle of refraction. 8. When the last angles of incidence of 40° has been tried, position the slit carefully by rotating the light source slowly beyond 40° angle unit the refracted ray is observed to just graze the flat surface of the semicircular lens, i.e., the angle of refraction is equal to 90°. Determine the angle of incidence corresponding to this position of the slit. This is called the critical angle. Record its value in the Worksheet. 9. Remove the semicircular lens together with the pins and the graphing paper carefully from the cardboard. Tape a new graphing paper on the cardboard and repeat step 1 on the new graphing paper. 10.Fill one half portion of the circular cuvette, corresponding to one semicircle, with water. Place the cuvette on the new graphing paper such that the center of the cuvette coincides with the point of intersection in the graphing paper. Let the half portion filled with water
be above the horizontal axis and the empty portion be below the axis as shown in Figure 4 below. 11.Repeat steps 3 to 8 above. Record the values obtained for the angle of refraction together with that of the critical angle for water. III. Results and Discussions IV. Conclusions
Based on the table shown in the results, we can conclude that light bends as it passed from one medium to another medium and the amount of bending depends on the indices of refraction of the two media.
