A-Level Physics May/June 2025 Q5(b)(ii): The amplitude of the incident light wave is A₀ when the intensity of the wave is I₀. Us…

1 answer

• ▲0
  accepted ✓

  The relationship between the intensity $I$ and amplitude $A$ of a wave is: $I \propto A^2$ [1]

  Malus's law gives the transmitted intensity $I$ through a polarising filter: $I = I_0 \cos^2 \theta$ [2]

  Here, $\theta$ is the angle between the plane of polarisation of the incident light and the transmission axis of the filter. From the context of the question, this angle is $90^\circ - \alpha$. $\theta = 90^\circ - 20^\circ = 70^\circ$ [3]

  We can combine the intensity-amplitude relation and Malus's law. Let the transmitted amplitude be $A$. $\frac{I}{I_0} = \left(\frac{A}{A_0}\right)^2$

  So, $\left(\frac{A}{A_0}\right)^2 = \cos^2(70^\circ)$ [4]

  Taking the square root of both sides: $\frac{A}{A_0} = \cos(70^\circ)$ $A = A_0 \cos(70^\circ)$ $A = A_0 \times 0.34202...$

  $A = 0.34 A_0$ (to 2 s.f.) [5]

  ---

  How the marks are awarded

  • C1 — Stating or using the relationship that intensity is proportional to amplitude squared ($I \propto A^2$).
  • C1 — Correctly stating or applying Malus's Law ($I = I_0 \cos^2 \theta$).
  • C1 — Correctly determining that the angle to be used in Malus's Law is $90^\circ - 20^\circ = 70^\circ$.
  • C1 — Correctly substituting the angle into the combined relationship, for example by showing $(A/A_0)^2 = \cos^2(70^\circ)$ or calculating the intermediate intensity ratio $I/I_0 \approx 0.12$.
  • A1 — Calculating the final correct amplitude as $0.34 A_0$.

  Common mistakes

  • Using the given angle $\alpha = 20^\circ$ directly in Malus's law instead of calculating the correct angle $\theta = 70^\circ$.
  • Forgetting to square the cosine term in Malus's law, incorrectly using $I = I_0 \cos \theta$.
  • Confusing the relationships for intensity and amplitude, for example by incorrectly writing $A = A_0 \cos^2 \theta$.
  • Forgetting to take the square root when converting from the intensity ratio to the amplitude ratio, leading to an incorrect answer of $0.12 A_0$.

  Examiner tip: Always determine the effect on intensity first using the relevant law (like Malus's law), and only then relate intensity to amplitude using the fundamental relationship $I \propto A^2$.

  ---

  AI-generated model answer, grounded in the official Cambridge mark scheme and reviewed by the MarkScheme team. Mark your own answer to this question →

  @markscheme_answers

Your answer

Sign in to answer this question.