Reflection and refraction of light

This laboratory exercise is one quantitative investigation of the reflection and refraction of light off optical interfaces. An optical interface is a boundary between two transparent media of different indices of refraction. Reflection makes mirrors, refraction eyeglasses and microscopes.

  1. Tape a sheet of quadrille paper onto the table. Record the label of your sample, a rectangular slab of transparent material, so later you can check the value of its index of refraction n against the manufacturer’s. Center this slab on the paper and tape it down. With pen or pencil mark its position onto the quadrille paper: draw a line against each of the four sides at their base. By positioning the laser pointer at various places in the upper left quadrant and aiming it at the slab, you can vary the angle of incidence θi1. Position the laser at the edge of the quadrille paper.
  2. Hold an index card in the path of the laser beam, so you can see where the laser hits. Every few centimeters between S (the mouth of the laser) and I (the point of impact on the slab) mark with a pencil the path of the light on the quadrille paper. [Hold the index card straight up, position it so one of its vertical edges just clips the ray of light, then mark the quadrille paper at the foot-corner of the index card.] Draw the best straight line through the marks. Does light travel in a straight line in the uniform medium of still air? Depending on the optical quality of your sample, you may or may not be able to see the laser beam traversing it: less than perfectly transparent materials, such as dusty air, may scatter enough light sideways to make the beam visible. Look down through the top of the sample, see if you can see the beam inside the slab, to ascertain if it travels in a straight line through this material as well.

Warning: never look a laser beam in the eye. Never point a laser beam at anyone’s eye. Permanent blindness may result.

  1. With the help of the index card locate I, the point of incidence on the interface, and another point several centimeters downstream of the reflected ray (upper right quadrant). Mark these two points on the quadrille paper and draw a straight line through them: the reflected ray. Measure the angle of reflection θr and compare it to the angle of incidence θi1. Hint: You can measure angles with the protractor provided, or by reading off the relevant lengths on the quadrille paper and using trigonometry. It would even be better to do both and compare, at least once.

We adopt the universal convention of measuring angles of all rays with respect to the local normals to the interfaces, the two dotted lines through I and E.

Estimate visually the intensity of the light reflected from the slab compared to the intensity of the incident ray: would you say it is less than 10%, about half, or more than 90%?

  1. Repeat step 3 on the ray of light transmitted through the sample that exits from point E (lower right quadrant). Compare the angle of exit θt2 to the angle of incidence θi1. Would you say the amount of light transmitted is less than 10%, about half, or more than 90% of the incident light? Is this estimate consistent with the one you made in step 3? Explain.

______

HOMEWORK 1. Use high-school geometry to show that θt1 = θi2.

______

HOMEWORK 2. Theoretically, the angle of reflection θr always equals the angle of incidence θi1. Theoretically, is the angle of exit θt2 always equal to the angle of incidence? Explain.

  1. By measuring w, the width of the slab, and d, the distance along the interface between the points of incidence (I) and exit (E), deduce the angle of refraction θt1. If your sample scatters enough light sideways to be seen looking down into it, then you can measure the angle of refraction directly with a protractor without measuring d.
  2. Repeat the measurements of the angles of reflection and refraction at three other values of the angle of incidence. Plot θr against θi1 and compare to the law of reflection. Plot sin θt1 against sin θi1 and compare to Snell’s law. From the latter plot deduce the index of refraction n of your material and compare to the value quoted. Take the index of refraction of air to be 1.
  3. Remove the sample. Prolong the line of step 1, the record of the incident ray. Measure x, the (perpendicular) distance between the incident and transmitted rays, at two different places along the rays: are these two rays parallel to each other? Have you not already checked this claim earlier? Compare x to your answer to Homework 3.

______

HOMEWORK 3. The slab is perfectly rectangular. Use high-school geometry and Snell’s law to show that the transmitted ray keeps the direction of the incident ray, only displaced sideways by a distance x. Calculate this displacement x in terms of the refractive index of the sample, its width, and the angle of incidence. Is rectangularity of the sample a condition a) necessary but not sufficient, b) sufficient but not necessary, c) necessary and sufficient, d) neither necessary nor sufficient, of parallelism between the incident and transmitted rays?

______

HOMEWORK 4. Given the equipment available: laser pointer, rectangular sample, protractor/ruler, index card, design your own experiment to observe total internal reflection and to measure the angle of total internal reflection. Hint: Total internal reflection occurs only when light goes from a denser medium (the sample) into one of lower index (air). The difficulty is that the laser pointer cannot be inserted into the sample.

  1. Do the experiment you have concocted in Homework 4. From the result calculate the index of refraction n and compare to the value obtained earlier.

θi1 (˚) / θr / θt2 / d / θt1 / sin θi1 / sin θt1
0

1