# Diffraction of Waves

## Diffraction of Waves Revision

**Diffraction of Waves**

Whenever **waves** pass through an opening they **diffract**. **Diffraction** is the process of waves spreading out and the extent of the **diffraction** is dependent on the **wavelength** of the wave and the size of the opening they are passing through.

**Single Slit Diffraction**

When the width of the opening is appropriately the same size as the **wavelength** of the wave, the greatest extent of **diffraction** can be seen. The bigger the opening in comparison to the **wavelength**, the less his effect is noticed.

**Diffraction** can be seen in the diagram below:

A laser can be passed through a single slit of opening similar to that of the **wavelength** of light from the laser. The diffracted light is projected onto a screen for analysis. A distinct **diffraction pattern** is seen on the screen.

If we conduct the same experiment but with light of a greater **wavelength**, we would see the same pattern but each fringe would be wider and the fringes further apart. This is because longer **wavelengths** diffract more than shorter ones.

If we kept the same blue laser with the same **wavelength** but narrowed the slit, the **fringe spacing **would be wider as more **diffraction** would occur and the intensity of all the fringes would decrease.

**Diffraction Gratings**

A **diffraction grating** is a plate with a large number of slits in it. The slits are very close together and the size of each slit is very narrow.

A **diffraction grating** also can be used to produce a **diffraction pattern** on a screen, as seen with the single slit. Areas of **maxima** (**constructive interference**) and **minima** (**destructive interference**) can be seen on a screen away from a central maxima.

An equation can be used for **diffraction gratings** which gives us the angle to the normal of each **maximum**:

dSin\Theta = n \lambda

- d= the
**space between each slit**in metres \text{(m)} - \Theta= the
**angle between the normal and the path to the maximum**in degrees (\degree) or radians \text{(rad)} - n= the
**order of maxima**, 0 being the central maximum, 1 being the first maximum etc - \lambda= the
**wavelength**of light in metres \text{(m)}.

**Example:**

A diffraction grating has slit separation of 1.5 \,\mu\text{m}. Monochromatic light of 400 \text{ nm} is passed through the diffraction grating to produce a diffraction pattern on a screen. Calculate the angle to the first maximum.

**[2 marks]**

\bold{dSin\Theta} = \bold{n\lambda}

Rearrange to find Sin\Theta:

\begin{aligned} Sin\Theta &= \dfrac{n\lambda}{d} \\ &= \dfrac{1 \times 400 \times 10^{-9}}{1.5 \times 10^{-6}} \\ &= 0.2667 \end{aligned} \\ \begin{aligned} \Theta &= Sin^{-1}(0.2667) \\ &= \bold{15.5 \degree} \end{aligned}

**Diffraction gratings** have many purposes:

- Produce
**spectrometers**(devices used to separate light of different wavelengths) **Analyse light**from stars- Analyse the
**composition**of stars **X-ray crystallography**

## Diffraction of Waves Example Questions

**Question 1:** What is diffraction and what conditions would cause the most diffraction to occur?

**[2 marks]**

Diffraction is the **spreading out of a wave** as it passes through a small gap. This occurs most when the **wavelength of the wave and the gap are similar in size**.

**Question 2:** Describe some of the uses of diffraction gratings.

**[3 marks]**

Any 3 uses from:

- Producing
**spectrometers**(devices used to separate light of different wavelengths) **A****nalysing light from stars****Analyse the composition of stars****X-ray crystallography**.

**Question 3:** A diffraction grating has slit separation of 2.1 \, \mu\text{m}. Monochromatic light of 600 \text{ nm} is passed through the diffraction grating to produce a diffraction pattern on a screen. Calculate the angle to the second maximum.

**[2 marks]**