More practice questions

4. Q4. Assertion: a well-cut diamond sparkles more than glass cut the same way. Reason: the critical angle of diamond is much smaller than that of glass. Are both true, and does the reason explain the assertion?

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   A smaller critical angle contributes to diamond’s sparkle, but observed brightness also depends on the cut, illumination and viewing direction. In the textbook comparison, with i_c = 24.41° against 41.14° for crown glass, more internal ray directions satisfy total reflection in diamond than in crown glass (reasoned from NCERT’s Summary, page 246, which names diamond’s multiple internal reflections, and the critical angles in NCERT Table 9.1, page 230).

5. Q5. Light goes from glass (n = 1.5) towards water (n = 1.33). Find the critical angle at the glass–water boundary.

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   sin i_c = n_water/n_glass = 1.33/1.5 ≈ 0.887, so i_c ≈ 62.5° (NCERT Eq. (9.12), page 230).

6. Q6. An optical fibre has a core of refractive index 1.50 and a cladding of 1.40. Find the critical angle at the core–cladding boundary.

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   sin i_c = 1.40/1.50 ≈ 0.933, so i_c ≈ 69.0°; light meeting the wall at more than this is totally reflected (NCERT Eq. (9.12), page 230).

7. Q7. Check NCERT Table 9.1’s critical angle for diamond (n = 2.42).

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   sin i_c = 1/2.42 ≈ 0.413, so i_c ≈ 24.4°, matching the table’s 24.41° (NCERT Table 9.1, page 230).