Diffraction Gratings

A diffraction grating is an optical plate that divides or disperses white light. As you know, white light is composed primarily of seven different colours, each with a different wavelength. The simplest type of grating is a structure with evenly-spaced identical slits.

When light passes through several openings, the light will refract around the openings. The waves that are created behind the openings will interfere with one another, merging together where two peaks meet to create a new peak of higher amplitude; this is also known as constructive interference. They interfere destructively when a trough and a peak meet. This creates an interference pattern, which is shown below.

This is the principle of a diffraction grating. When a parallel beam of light is directed at a diffraction grating with several identical openings, this will result in an interference pattern of bold and faint points of light.

What is a diffraction grating pattern?

When white light is incident on a parallel grating plate with several or even hundreds of evenly-spaced identical slits, it is diffracted creating spherical waves around the openings that interfere with one another. This creates an interference pattern, where each wave interacts with another. This further creates a pattern of maximums and minimums, as seen below.

The light that is shown on the back screen is a series of dots called maximums. The empty space in between the maximums is called the minimum. The maximum that is parallel to the light beam is the zero-order maximum, while the dots on the sides are the first and the second order maximums going outwards from the middle. The visible points are those points at which many different rays of light interfered.

The angles at which the maximum intensity points occur are known as fringes, and can be calculated using the grading equation below.

\[d \cdot \sin\theta = n \cdot \lambda\]

where d is the spacing between the slits in metres, θ is the separation angle between the order of maximum in degrees, n is the order of maximum, and λ is the wavelength of the source in metres.

Therefore, \(\sinθ\) is proportional to the wavelength, which means the longer the wavelength of light (red light has the longest wavelength), the greater the angle. It can also be derived from the above equation that the larger the number of slits per metre (hence, the smaller the d component), the bigger the angle of diffraction.

Diffraction grating diagram

For conducting the experiment, position a white light source opposite a diffraction grating. A wall behind the grating will be used as a projection screen. Secure the light source with tape and the diffraction grating with binder-type clips. Position a piece of coloured plastic or colour filter between the source and the diffraction grating as needed.

Methodology

1. Direct the white light beams through the diffraction grating and observe the pattern projected on the wall. Adjust the angle between the beam of light and the glass as needed to achieve the diffraction grating pattern required.

2. Identify the zero-order beam and the diffracted beams by the intensity in the spots illustrated on the wall.

3. Using a ruler, measure distance between the glasses and the white spot on the screen.

4. Repeat the experiment with several laser pointers.

5. For each different light beam, measure the distance between the straight unbent beam and the diffracted beams, also known as h.

6. Calculate the wavelength and compare it to the manufacturer's wavelength, which is the wavelength of the laser used.

7. Insert a piece of coloured cellophane plastic or filter, between the white light beam and the diffraction grating. Record any observations.

Observations

• The wavelength is calculated by rearranging the equation so that λ is the subject. Using trigonometry angle θ can be found.
• The distance D is shown below, which can be used to find the separation angle.
• The wavelength can be determined using the equation below, where a triangle is shaped between the distance from the grating to the wall and the fringe spacing shown in figure 7 as h.

\[\tan \theta = \frac{h}{D} \lambda = \frac{d \cdot \sin \theta}{ n}\]