In an experiment to measure the wavelength of monochromatic light, a diffraction pattern was produced using a diffraction grating with 500 lines per mm - Leaving Cert Physics - Question 3 - 2008

The first order images were identified by locating them nearest to either side of the brightest or central maximum, which corresponds to the zero order image. It can be affirmed that these images represent the first diffraction maxima on either side of the central peak.

The angle between the first order images was measured using the following procedure:

1. Set up: Ensure the laser is focused on the first order image while noting the position on the spectrometer scale for the left position of the first order image.
2. Measure: Record this reading and align the laser beam to the other first order image to get its position on the scale.
3. Subtract: The difference between these two readings gives the angle between the first order images.

To calculate the wavelength, use the formula:

n heta = rac{n ext{d}}{ ext{λ}}

Where:

• $n$ is the order of the image,
• $heta$ corresponds to the angle, and
• $d$ is the distance between the grating lines.

Using the first order image with $heta = 34.2°$, we can input the provided values:

• Given: Number of lines = 500 lines/mm, thus, d = rac{1}{500 imes 10^3} = 2 imes 10^{-6} m.
• For first order ($n=1$):

ext{λ} = rac{d imes ext{sin}( heta)}{n}

Calculating further: ext{λ} = rac{2 imes 10^{-6} imes ext{sin}(34.2°)}{1} $ext{λ} ≈ 5.88 imes 10^{-7} m$

This process is repeated for the additional angles, leading to an average calculated wavelength after averaging results:

• Final average = 585 ± 2 nm.