# Laser interference

## What is interference?

When a wave hits a small obstacle, it diffracts around it. This causes interference to appear as the diffracted waves meet each other. The pattern of interference depends on the size of the object. See Figure 1.

Light is an electromagnetic wave. When a laser hits a small object, we can observe a pattern of spots on a faraway wall. This is the exact same interference! See Figure 2.

To see interference, the object cannot be much larger than the wavelength λ of the light. If we know the wavelength, we can measure the interference pattern to measure the object’s size. See Figure 3.

The wavelength of red laser light is approximately 650 nm (nanometres), and the wavelength for green is around 532 nm. One nanometre is one billionth of a metre, so this kind of interference is only noticeable for small objects.

Figure 1 Wave interference from two sources

Figure 2 Laser interference after passing through a slit

Figure 3 A transverse wave with wavelength λ

## Activity: Measuring the Width of a Hair

A human hair is too thin to measure directly with a ruler. Can we measure it using light interference?

### Materials

You will need:

• a laser pointer
• measuring tape
• a calculator
• construction materials (e.g., tape, scissors, clips)
• a strand of hair

### Steps

1. Mount the hair vertically using tape, cards, and other supplies.

2. Create a long, clear path from the mount to a flat wall. Measure the distance “d” from the hair to the wall (in centimetres).

3. Have a partner shine the laser on the wall through the hair.

4. Observe the pattern on the wall, and measure the separation “s” between the dark spots (in centimetres). The pattern will be easier to see in a dark room. Calculate the width of the hair as

Most human hairs are between 0.01 and 0.001 centimetres. What else can be measured using this method?

### What happened?

Without the hair in the way, the laser should make a nice clean circular spot on the wall. However, when the hair is introduced, an interference pattern shows up on the wall. This is because the laser light diffracts around both edges of the hair, and those two diffraction patterns interfere with each other. We see dark spots at areas of destructive interference, and bright spots at areas of constructive interference.

#### Laser diffraction

You might ask why blocking light seems to create more light. If we were to use a sensitive light meter, we would find that there’s actually less light power in the pattern than there was in the laser originally, as the hair absorbs some light. However, the presence of the hair spreads out the light intensity over a much wider area.

The spacing of the interference pattern from the hair is the same spacing we would expect for a narrow opening of the same width. Just as we can use this technique to measure small objects, we can also use it to measure small openings. This duality between objects and openings is known as Babinet’s Principle.

#### Diffraction-based security

More complex patterns can arise from more complex structures. Sometimes, this can be used to identify objects. Different crystals produce different interference patterns when laser light shines through them. This can even be used for security. Modern Canadian bills have interference signatures programmed into them. Try shining the laser through the centre of the maple leaf and looking at the pattern it makes on the wall.

## Quantum connection

Diffraction patterns like these can be used to measure the size of small objects and identify the structure of complex crystals.

We can also see interference patterns with other quantum particles, like electrons, atoms, and even large molecules! This shows that matter, on the quantum level, can behave like a wave.