A student used a narrow beam of monochromatic light and a diffraction grating to determine $\: \\lambda$, the wavelength of the monochromatic light - Leaving Cert Physics - Question 3 - 2018

To find the angle, the student measured two distances:

1. $s_1$: the distance between the diffraction grating and the screen, recording $heta_1$ at n=1 to the left.
2. $s_2$: the distance between the first order images, recording $heta_2$ at n=1 to the right.

The angle $heta$ between the images is then calculated as:

$heta = heta_2 - heta_1$

Given the number of lines per mm, we convert this to meters:

• Number of lines per meter $d = 2 imes 10^{-6}$ m.

Using the formula: $n imes d = ext{sine } heta$ Substituting the values:

• First order: $n = 1$
• Angle: $heta = 17.05°$

Calculating the wavelength:

$\theta$ decreases if the number of lines per mm increases, as the greater number of lines results in a finer grating.

The grating with 500 lines per mm gives larger measurements with smaller percentage error when compared to the 80 lines per mm grating.

The student would observe a spectrum of colors rather than distinct bright images, as white light consists of multiple wavelengths.