A student investigates interference of light by directing laser light of wavelength 630 nm onto a grating as shown - Scottish Highers Physics - Question 8 - 2018

Using the grating equation: $m \lambda = d \sin(\theta)$ where:

• $m = 3$ for the third order maximum,
• $\\lambda = 630 \times 10^{-9} m$ (wavelength), and
• $d = \frac{1}{250 \times 10^3} m$ (grating spacing).

Substituting the known values yields: $3 \cdot 630 \times 10^{-9} = \frac{1}{250 \times 10^3} \sin(\theta)$

Solving for $\theta$ gives: $\theta = \sin^{-1}(\frac{3 \cdot 630 \times 10^{-9}}{\frac{1}{250 \times 10^3}}) = 28^{\circ}$.

The spots will be further apart when using the new grating with 600 lines per millimetre.

This is because the slit separation of the new grating is larger than that of the previous grating, leading to a greater angle for each order maximum according to the grating equation.

Coherent light refers to light waves that have a constant phase relationship and the same frequency and wavelength.

The pattern observed with the £5 note may result from the polymer structure of the note, which creates a different pattern of interference due to its physical characteristics compared to the regular grating, which is designed specifically for light interference patterns.