A diffraction grating has 500 lines per mm - AQA - A-Level Physics - Question 17 - 2018 - Paper 1

To find the wavelength of the monochromatic light, we can use the diffraction grating equation:

$d \sin(\theta) = m \lambda$

Where:

• $d$ is the distance between grating lines,
• $\theta$ is the diffraction angle,
• $m$ is the order of the spectrum (in this case, $m = 3$), and
• $\lambda$ is the wavelength.

1. Calculate $d$: Given that there are 500 lines per mm, the distance between grating lines, $d$, can be calculated as: $d = \frac{1}{500 \text{ lines/mm}} = 0.002 ext{ mm} = 2 \times 10^{-6} ext{ m}$

2. Use the Diffraction Equation: Plugging in the known values into the diffraction equation:

   $2 \times 10^{-6} \sin(60°) = 3 \lambda$

3. Calculate $\sin(60°)$: This gives: $\sin(60°) = \frac{\sqrt{3}}{2}$

4. Rearranging the Equation for $\lambda$: Now we can rearrange the equation to find $\lambda$: $\lambda = \frac{2 \times 10^{-6} \cdot \frac{\sqrt{3}}{2}}{3} = \frac{\sqrt{3} \times 10^{-6}}{3} m$

5. Convert to nm: Calculating this gives us:

   $\lambda \approx 0.577 \times 10^{-6} m = 577 nm$

By selecting the closest option from the given choices, we find the wavelength of the monochromatic light is approximately 580 nm, thus the correct answer is B.