In an experiment to measure the wavelength of a monochromatic light source, a narrow beam of light was incident normally on a diffraction grating having 400 lines per mm - Leaving Cert Physics - Question 3 - 2011

To obtain the data for measuring the angles, the following steps were used:

1. Set up a monochromatic light source, a spectrometer, and a diffraction grating on a turntable.
2. Ensure that the light beam is focused on the first image on the left-hand side (l.h.s) scale.
3. Measure the angle θ using trigonometry with reference to the distance D from the grating to the measurement screen. A diagram representing this setup is crucial for clarity.

Using the formula for diffraction:

$n d = D imes ext{sin} heta$

Where:

• n = order of the image (n=1 for the first image, n=2 for the second image)
• d = distance between lines on the grating = 1 / 400 mm
• D = distance to the screen (this is measured) Using the angles:
• For the first image (${θ = 14.90°}$): d = rac{1}{400} ext{Wavelength } ext{λ} = rac{D imes ext{sin}(θ)}{n} Calculating for average angle yields: $ext{Wavelength } ext{λ} ext{ approximately equal to } 642.3 ext{ nm}$.

i) Using a monochromatic light source of longer wavelength:

• This would result in fewer images or a wider spacing between them, as longer wavelengths lead to less diffraction.

ii) Using a diffraction grating having 200 lines per mm:

• This would yield smaller or closer images due to increased diffraction effects as it allows for a more substantial interaction with the incoming light.

iii) Using a source of white light instead of monochromatic light:

• In this scenario, each fringe/image would represent a spectrum formed due to the different wavelengths present in white light, leading to the overlapping of colors which could blur the bright images.