This is an old revision of the document!

# PHY124 Lab 7 - Reflection, Refraction and Images

There are two parts to this lab which can be done in either order In Part I you will study the Laws of Reflection and Refraction, measure the index of refraction of glass and observe dispersion. In Part II you investigate images produced by lenses.

## Part I

### Equipment

• “Ray” table
• Triangular prism

### The laws of reflection and refraction

When the light beam hits the air–glass boundary, side 1 of the prism in Fig. 2 above, reflection and refraction occurs (see Ch21 sheet 8,9). A small fraction of the intensity of the incident beam is reflected, leaving a faint reflected ray outside the prism, and the remainder of the intensity is refracted into the prism. The refracted ray hits the glass-air boundary on side 3 of the prism and the ray is again refracted into the air as the “exit” ray in Fig. 2 above. The ray reflected inside the prism on boundary 3 is barely visible.

The law of reflection states that the incident angle $\theta_{i}$ equals the angle of reflection $\theta_{r}$ (Ch21 sheet 8)

$\theta_{i}=\theta_{r}$
(7.1)

For refraction, Snell’s Law holds. Snell’s Law is given on Ch21 sheet 9;

$n_{1}\sin\theta_{1}=n_{2}\sin\theta_{2}$
(7.2)

In our case for boundary 1 $n_{1}$ is the index of refraction of air (which we assume to be 1 as for vacuum) and $n_{2}$ is the index of refraction of glass. In this lab $n_{2}$ is considered to be unknown and you will be measuring it by applying Snell’s Law on boundaries 1 and 3.

### Procedure

Make sure the lamp is as close as possible to the slits. Using a piece of paper, block all beams except the central beam, then place a sheet of paper onto the trace table (secure it with the clamps on each corner). Position the triangular prism so that side 1 is ~45o with respect to the incident ray direction as shown in Fig. 2 above. Trace the incident, reflected and exit rays (shown in Fig. 2) and trace the outline of the prism.

Closely inspect the exit ray. You should notice that it has a blue side and a red side. On your sketch, record which side of the exit ray shows which color. You will use this information during Section 3 of Part I, which deals with dispersion.

Make sure your paper stays fixed in place while you are tracing.

#### 1. The Law of Reflection

First, take your sketch and add “normal” lines (lines perpendicular to where the rays hit the boundaries) to the sides 1 and 3. Since light will travel in a straight line, connect the incident from where it hits side 1 and the exit ray from where it hits side 3. This will be the path of the light ray inside the prism. Find the angles of incidence and reflection for the incident ray. Make sure you take these angles with respect to the normal line you drew! Measure the angles of incidence and reflection and include an estimate of the error with your values. Check them against the Law of Reflection, ie. Are the two angles equal within error?

#### 2. Snell’s Law

Measure the angles of incidence and refraction on boundaries 1 and 3 (again with respect to the normal lines you drew). Use Snell’s Law to calculate the index of refraction of the prism glass for both boundaries

Be Careful! Make sure you pay attention to which index of refraction you use for glass and air for the two separate cases. For the side 1 boundary $n_{1}$ should be for air and $n_{2}$ should be for glass. For the side 3 boundary $n_{1}$ should be for glass and $n_{2}$ should be for air.

#### 3. Dispersion: qualitative only

The index of refraction depends slightly on the wavelength of light. Thus light with different wavelengths (and hence different color) is bent by different angles. When you looked at the exit ray and saw different colors being refracted at slightly different angles you were observing dispersion (seeCh21 sheet 9’).

Which color is bent more, red or blue? Which light has the larger index of refraction, red or blue light (hint: Look at Snell’s Law)?

#### 4. Total Internal Reflection: qualitative only

For a critical angle of incidence $\theta_{c}$ on the glass-air boundary 3 no refracted intensity is visible, the full intensity of the incident beam is reflected back into the glass. At the angle with this happens, total internal reflection occurs.

Place a new sheet on the ray table and slowly rotate the prism slowly clockwise from the position it had for the measurements above (~45o) with respect to the incident beam from the slit). As you rotate the prism you should notice that the exit ray makes smaller and smaller angles with boundary 3. You should also observe a beam exiting boundary 2. Observe the intensity of the beam coming from side 2 as you continue to turn the prism. Rotate the prism until the exit ray disappears completely, while observing the intensity of the new ray from boundary 2. Rotate back and observe a couple of times.

Describe your observations of the intensity of the beam emanating from boundary 2 as you rotate the prism. When the “exit ray” in Fig 2 disappears, is the intensity of the beam emanating from boundary 2 maximal or minimal? On which boundary do you observe total internal reflection?

## Part II

### Equipment

• 1 “Optical Bench: a rail to mount the holders of lenses/screen on
• 1 Box with lenses (Use #3 and # 4 only – marked at bottom of shaft)
• 2 Holders for lenses/screen
• 1 Screen
• 1 Lamp with arrow (our object to be imaged)

Verify that you have the correct lens mounted before you start measuring! The lenses are marked at the bottom of the shaft of the lens holder: #3: 10 cm diverging lens #4: 5 cm converging lens 