# 5.11.5 Transmission Diffraction Grating

## Transmission Diffraction Grating

• Dispersion is the separation of visible white light into a spectrum of its colours
• This can be done using a glass prism or a diffraction grating
• Transmission diffraction gratings are useful for separating light of different wavelengths with high resolution in order to:
• Analyse light from stars
• Analyse the composition of a star Diffraction gratings are most commonly used in spectrometers to analyse light from stars

• A transmission diffraction grating is a glass or plastic slide containing a large number of regularly spaced, parallel slits or lines
• It is used to analyse spectral line wavelengths from the light emitted by stars
• The angular dispersion (separation) of the colours is much greater using a transmission diffraction grating than an optical prism
• Using diffraction gratings results in sharper fringes compared to using a double slit

## Condition for Maxima for a Diffraction Grating

• The angles at which the maxima of intensity (constructive interference) are produced can be deduced by the diffraction grating equation: • Exam questions sometime state the lines per m (or per mm, per nm etc.) on the grating which is represented by the symbol N
• d can be calculated from N using the equation #### Angular Separation

• The angular separation of each maxima is calculated by rearranging the grating equation to make θ the subject
• The angle θ is taken from the centre meaning the higher orders are at greater angles Angular separation

• The angular separation between two angles is found by subtracting the smaller angle from the larger one
• The angular separation between the first and second maxima n1 and n2 is θ2θ1

#### Orders of Maxima

• The maximum angle to see orders of maxima is when the beam is at right angles to the diffraction grating
• This means θ = 90o and sin θ = 1

• The highest order of maxima visible is therefore calculated by the equation: • Note that since n must be an integer, if the value is a decimal it must be rounded down
• E.g If n is calculated as 2.7 then n = 2 is the highest order visible

#### Worked example

An experiment was set up to investigate light passing through a diffraction grating with a slit spacing of 1.7 µm. The fringe pattern was observed on a screen. The wavelength of the light is 550 nm. Calculate the angle α between the two second-order lines. #### Exam Tip

Take care that the angle θ is the correct angle taken from the centre and not the angle taken between two orders of maxima. ### Get unlimited access

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