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# Inquiry: Index of Refraction

## Procedure:

The index of refraction of a substance is defined as the ratio of the speed of light in a vacuum to its speed in that substance. Since the speed of light in air is only slightly different from the speed in a vacuum, a negligible error is introduced when we measure the index of refraction by permitting light to travel from air into another medium. Snell provided a simple direct method of measuring the index of refraction by defining it in terms of functions of the angle of incidence and the angle of refraction. The mathematical relationship, known as Snell's law, is:

## n1 (sin Θ1) = n2 (sin Θ2)

We will be using what we call the circle method to determine the index of refraction of the glass square and triangle. In the picture below, the sine of both angles would be the opposite side over the hypotenuse which are both the radius of the circle and are equal. Therefore the index of refraction of the glass can be calculated by dividing the green line in the air by the green line in the glass. Basically you always divide the biggest line by the smallest line because your index of refraction must always be greater than one. The index of refraction of glass varies with its composition and with the wavelength of the light incident on the glass. Your experimental results should be precise enough to enable you to identify the kind of glass used in this experiment.

## Inquiry Questions: Part 1

Place the glass square on the center of a sheet of paper and outline it with a pencil. Place pin B next to the glass app. 1 cm in from the lower left hand corner. Place pin A next to the glass app 1 cm in from the upper right hand corner. Now kneeling down to look through the edge of the glass, place a pin C not less than 7 cm from B so that A is in line with B and C as seen through the glass square. Keep the eye you sight with near the level of the tabletop. Remove the glass plate, and join the points A, B and C to represent the path of the light traveling from the pin C through the air to pin B and through the glass to pin A. Identify the incident ray and the refracted ray. From B construct a normal line to the plate of glass. Using as large a radius as possible, draw a circle with point B as the center, which intersects the normal and the rays of light. Construct perpendicular lines from the normal lines to the points of intersection of the circle with the rays of light. These are the lines opposite the angles in the diagram. Measure the length of these lines to the nearest millimeter and compute the index of refraction by dividing the longest line by the shortest line and record in the data table as index1. By means of a protractor, measure the angles from this data and find the index of refraction of the glass square again by dividing sin Θ1/ sin Θ2 and record in the table as index2.

## Inquiry Questions: Part 2

Arrange the glass triangle on another piece of paper and proceed to determine the index of refraction using the same method. Depending on the angle that you look through the triangle you will see two pins. Locate both of these images. Decide which is the correct image to determine the index of refraction . From this index of refraction determine the critical angle. Using this critical angle and the drawing of your other image, explain why you get two images.

## Inquiry Questions: Part 3

Draw a tiny x on a sheet of paper and stand the glass plate up on edge over the x. Now, looking down through the glass plate you will notice that the x seems like it is hovering on a strip of paper closer to you. As best you can by holding your pencil at the side of the glass try to find the distance from the top of the glass down to the image of the x. This is d. The actual height of the glass is given by D. A simple relationship is given below to determine the index of refraction. Compare it to what you got in PART 1.