Resonance

Experiment 10. Geometrical Optics

This laboratory is to demonstrate how the very simple principles of reflection and refraction lead to sophisticated optical instruments.

Equipment

Ray box, white light source,
1 mirror, 1 protractor, 1 glass prism
Optical bench
3 converging lenses, 1diverging lens
2 lens holders
Ground glass screen with holder,.

Method

We begin with a ray box that has a slotted mask in front of a light bulb to produce a set of narrow beams (or "rays") of light. The rays lie along a plane surface (a sheet of paper). Your measurements will consist of pencil marks on the piece of paper, recording the direction of these rays before and after they strike a mirror or glass prism. Then you will progress to the study of lenses. Lenses are in essence refracting objects with precisely machined curved surfaces. Finally, you will construct simple two-lens optical instruments, a microscope and telescope.

Procedure

1. Light Wave Reflection

Use the ray box, a mirror, and protractor to verify that q_incident = q_reflected. Do this for at least three different incident angles q_incident.

2. Light Wave Refraction

A. Snell's Law

Use the ray box, a glass prism, and protractor to verify Snell's Law about refraction:

n_inc sin q_inc = n_refr sin q_refr,

where n_inc and n_refr are the refractive indices of the incident and refracting media, respectively. Take n_air = 1 and n_glass ~ 1.5.

Q1. Plot sin q_inc versus sin q_refr for at least three different angles sin q_incident. How can you use this plot to determine the index of refraction? B. Critical Angle

Snell's Law also tells us that if we reverse things, i.e. let light hit a glass-air boundary from within the glass, then:

sin q_incidentt/ sin q_refr= n_air/n_glass ~ 1/1.5 = 0.67

Now, because sin q_incident/ sin q_refr has a maximum of 1 (for q_refr= 90^o), there is a maximum on sin q_incident = _tn_air sin q_refr /n_glass ~ 0.67. The corresponding angle q_incidentfor which this happens is given the name critical angle, since refraction cannot occur for incident angles larger than sin q_critical = 1/n_glass. Therefore light hitting the glass-air interface at angles larger than q_critical stays trapped inside the glass; it is totally reflected. This effect is the basis for efficient transmission of light through glass fibers in modern communication technology.

Q2. Use your prism to determine q_critical and its uncertainty. Compare the measured value with what you expect on the basis of the equation above. C. Dispersion

Use the prism to observe light dispersion, i.e. the variation of the refraction index with the frequency of the light (or equivalently, the variation of the speed of light in material with the frequency).

Q3, Which colors are bent most? From measured angles, deduce n_blue and n_red for your prism. 3. Lenses

The apparatus consists of an optical bench which serves as a convenient holder for objects, lenses, and a ground glass screen for locating (real) images. The object is an arrow painted on a piece of ground glass illuminated from behind by a collimated light source. Your apparatus should include three converging lenses and one diverging lens.

Q4. Devise a method for determining the focal length of each lens. Use whatever method you please, but clearly describe your technique, and make sure and prove that it is accurate to at least ±1 cm. Keep in mind some useful formulae: m = s/s' and 1/f = 1/s + 1/s'. Here m is the magnification, s is the distance between the object and the lens, s' is the distance between the image and the lense, and f is the focus length.

4. Simple Microscope

Use the two shortest focal length converging lenses to make a compound microscope. Figure out a way to measure the linear magnification accurate to about ±30%. Make a sketch showing the object, intermediate and final image, and the chosen positions of your lenses.

Web page created by Laszlo Mihaly, September, 1999