Q4. Assertion: a single polaroid turned in front of a sodium lamp does not change the brightness seen through it. Reason: the lamp’s light is unpolarised. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: unpolarised light has its field in all directions equally, so every setting of the polaroid passes half of it (NCERT page 270).
Q5. At what angle between two polaroids does one eighth of the unpolarised light falling on the first come through the second?
(1/2) cos2 θ = 1/8, so cos2 θ = 1/4, cos θ = 1/2 and θ = 60° (NCERT Eq. (10.18), page 270).
Q6. Unpolarised light passes three polaroids; each pass axis is turned 30° from the one before. What fraction gets through?
1/2 × cos2 30° × cos2 30° = 1/2 × 3/4 × 3/4 = 9/32 ≈ 0.28 (reasoned from NCERT Eq. (10.18), page 270).
Q7. In NCERT Example 10.2, at what angle θ does half of the greatest possible light come through P3?
(I0/4) sin2 2θ = I0/8 gives sin2 2θ = 1/2, so 2θ = 45° and θ = 22.5° (or 67.5°) (NCERT Example 10.2, page 271).