# 2.20 Core Practical 6: Investigating Diffraction Gratings

## Core Practical 6: Investigating Diffraction Gratings

#### Aim of the Experiment

• To find the wavelength of light using a diffraction grating

Variables

• Independent variable = Distance between maxima, h
• Dependent variable = The angle between the normal and each order, θn (where n = 1, 2, 3 etc)
• Control variables
• Distance between the slits and the screen, D
• Laser wavelength, λ
• Slit separation, d

#### Equipment List • Resolution of measuring equipment:
• Metre ruler = 1 mm
• Vernier Callipers = 0.01 mm

#### Method The setup of apparatus required to measure the distance between maxima h at different angles θ

1. Place the laser on a retort stand with the diffraction grating in front of it
2. Use a set square to ensure the beam passes through the grating at normal incidence and meets the screen perpendicularly
3. Set the distance D between the grating and the screen to be 1.0 m using a metre ruler
4. Darken the room and turn on the laser
5. Identify the zero-order maximum (the central beam)
6. Measure the distance h to the nearest two first-order maxima (i.e. n = 1, n = 2) using a vernier calliper
7. Calculate the mean of these two values
8. Measure distance h for increasing orders
9. Repeat with a diffraction grating with a different number of slits per mm
• An example table might look like this: #### Analysing the Results

The diffraction grating equation is given by:

nλ = d sin θ

• Where:
• n = the order of the diffraction pattern
• λ = the wavelength of the laser light (m)
• d = the distance between the slits (m)
• θ = the angle between the normal and the maxima (°)

• The distance between the slits is equal to: • Where
• N = the number of slits per metre (m–1)

• Since the angle is not small, it must be calculated using trigonometry with the measurements for the distance between maxima, h, and the distance between the slits and the screen, D • Calculate a mean θ value for each order
• Calculate a mean value for the wavelength of the laser light and compare the value with the accepted wavelength
• This is usually 635 nm for a standard school red laser

#### Evaluating the Experiments

Systematic errors:

• Ensure the use of the set square to avoid parallax error in the measurement of the fringe width
• Using a grating with more lines per mm will result in greater values of h. This lowers its percentage uncertainty

Random errors:

• The fringe spacing can be subjective depending on its intensity on the screen, therefore, take multiple measurements of w and h (between 3-8) and find the average
• Use a Vernier scale to record distances w and h to reduce percentage uncertainty
• Reduce the uncertainty in w and h by measuring across all visible fringes and dividing by the number of fringes
• Increase the grating to screen distance D to increase the fringe separation (although this may decrease the intensity of light reaching the screen)
• Conduct the experiment in a darkened room, so the fringes are clear

#### Safety Considerations

• Lasers should be Class 2 and have a maximum output of no more than 1 mW
• Do not allow laser beams to shine into anyone’s eyes
• Remove reflective surfaces from the room to ensure no laser light is reflected into anyone’s eyes

#### Worked example

A student investigates the interference patterns produced by two different diffraction gratings. One grating used was marked 100 slits / mm, and the other was marked 300 slits / mm. The distance between the grating and the screen is measured to be 3.75 m.

The student recorded the distance between adjacent maxima after passing a monochromatic laser source through each grating. These results are shown in the tables below.  Calculate the mean wavelength of the laser light and compare it with the accepted value of 635 nm. Assess the percentage uncertainty in this result.    #### Exam Tip

Remember to read the question carefully and make sure dimensions such as the fringe separation are put into meters. ### Get unlimited access

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