A-Level Physics May/June 2024 Q6(a): The light has wavelength 520 nm. The separation of the lines in the grating is 3.8 × 10…

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  The relationship between the grating spacing $d$, the angle of diffraction $\theta$, the order number $n$ and the wavelength $\lambda$ is given by the diffraction grating equation:

  $d \sin\theta = n\lambda$

  To find the maximum possible order number, $n_{max}$, we consider the maximum possible angle for diffraction, which is $\theta = 90^{\circ}$. At this angle, $\sin\theta = 1$.

  Rearranging the formula for $n$ and substituting the values:

  $n = \frac{d \sin\theta}{\lambda}$

  $n_{max} = \frac{(3.8 \times 10^{-6}) \times \sin(90^{\circ})}{520 \times 10^{-9}}$

  $n_{max} = 7.307...$

  Since the order number $n$ must be an integer, the highest order of bright fringe that can be observed is $n=7$.

  Bright fringes are formed symmetrically on either side of the central maximum (where $n=0$). So, there are 7 orders on the positive side ($n=1$ to $7$), 7 orders on the negative side ($n=-1$ to $-7$), plus the central maximum ($n=0$).

  Total number of bright fringes = $(2 \times 7) + 1 = 15$.

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  How the marks are awarded

  • C1 — Stating the correct diffraction grating equation, $d \sin\theta = n\lambda$.
  • C1 — Correctly substituting values into the equation, using the condition for the maximum angle ($θ = 90°$), to find the maximum possible order number ($n=7.3...$).
  • A1 — Using the calculated integer value for the highest order ($n=7$) to determine the total number of fringes as 15, by calculating $(2 × 7) + 1$.

  Common mistakes

  • Forgetting to include the central (n=0) fringe, leading to an incorrect answer of 14 (from 2 × 7).
  • Incorrectly rounding the maximum order number up to 8, leading to a final answer of 17 (from (2 × 8) + 1).
  • Stating the answer as 7, which is the maximum order number, not the total number of fringes.
  • Forgetting to convert the wavelength from nanometres (nm) to metres (m) during the calculation.

  Examiner tip: For 'total number' questions in diffraction, always calculate the maximum order by setting θ = 90°, take the integer part, and then use the formula 2n + 1 to find the total.

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