A ray of monochromatic light is incident on a grating - Scottish Highers Physics - Question 15 - 2023

To find the maximum order of interference, we can use the formula:
$d \sin(\theta) = m \lambda$
where:
d = 5.0 \times 10^{-6} , \text{m}, \theta = 29^{\circ}, \lambda = 605 , \text{nm} = 605 \times 10^{-9} , \text{m}.$$

First, calculate ( \sin(29^{\circ}) ):
$\sin(29^{\circ}) \approx 0.4848$
Now plug this into the formula to find m:
$m = \frac{d \sin(\theta)}{\lambda} = \frac{(5.0 \times 10^{-6}) (0.4848)}{(605 \times 10^{-9})}$
Calculating this gives:
$m \approx \frac{2.424 \times 10^{-6}}{6.05 \times 10^{-7}} \approx 4.01.$

Thus, the maximum order of interference is m = 4.