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JEE Physics 2023 Question with Solution

Given below are two statements: Statement I: If the Brewster's angle for the light propagating from air to glass is θb\theta_b, then Brewster's angle for the light propagating from glass to air is: π/2−θb\pi/2 - \theta_b Statement II: The Brewster's angle for the light propagating from glass to air is tan⁡−1(μg)\tan^{-1}(\mu_g), where μg\mu_g is the refractive index of glass. In the light of the above statements, choose the correct answer from the options given below:

  • A

    Both Statement I and Statement II are true.

  • B

    Statement I is true but Statement II is false.

  • C

    Statement I is false but Statement II is true.

  • D

    Both Statement I and Statement II are false.

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: Brewster's angle for light propagating from air to glass is θb\theta_b.

Find: Which statement is correct.

Statement I is correct. The Brewster's angle for light propagating from glass to air is given as

π2−θb\frac{\pi}{2} - \theta_b

where θb\theta_b is the Brewster's angle for light propagating from air to glass.

Statement II is incorrect. The Brewster's angle for light propagating from glass to air is not tan⁡−1(μg)\tan^{-1}(\mu_g). The correct expression for the Brewster's angle involves the relative refractive indices of the two media.

Therefore, Statement I is true and Statement II is false. The solution marks the correct option as C, which conflicts with the listed options; the defensible matching option among the given choices is B.

Option Discrepancy Note

Given: The listed options state that option B is "Statement I is true but Statement II is false."

Find: Resolve the mismatch between the option text and the solution label.

The solution explanation clearly concludes that Statement I is true and Statement II is false. However, the solution says "The Correct Option is C". Since option C in the listed options says "Statement I is false but Statement II is true," the header label does not match the written explanation.

Hence, based on the solution working and conclusion, the correct answer should correspond to B among the provided options.

Common mistakes

  • Assuming that the Brewster's angle remains the same when the direction of propagation is reversed is incorrect because the two media exchange roles. Use the complementary-angle relation for the reversed path instead.

  • Using tan⁡−1(μg)\tan^{-1}(\mu_g) directly for light going from glass to air is wrong because Brewster's condition depends on the ratio of refractive indices of the second medium to the first medium. Always identify the incident medium first.

  • Choosing the option only from the solution's letter label without checking the statement content can lead to an incorrect marked answer here. Match the conclusion of the explanation with the actual option text when there is a discrepancy.

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