Q4. Assertion: when light bends towards the normal on entering a medium, its speed in that medium is less. Reason: in Huygens’ construction, sin i/sin r = v1/v2. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: r < i makes sin i/sin r > 1, so v1 > v2 (NCERT Eq. (10.3), page 259).
Q5. Light passes from glass, where its speed is 2.0 × 108 m/s, towards water, where it is 2.25 × 108 m/s. Find the critical angle at the glass–water surface.
sin ic = n2/n1 = v1/v2 = 2.0/2.25 ≈ 0.889, so ic ≈ 62.7° (NCERT Eqs. (10.3) and (10.8), pages 259–260).
Q6. A wavefront in air meets water at i = 60°. Through what angle does the wavefront turn? Take n = 1.33.
sin r = sin 60°/1.33 ≈ 0.651, so r ≈ 40.6°. The wavefront makes 60° with the surface before and about 40.6° after, so it turns through about 19.4°, the same as the ray (NCERT Eq. (10.6), page 259).
Q7. A ray through the centre of a convex lens crosses 6.0 mm of glass (n = 1.5); a ray near the edge crosses 1.0 mm. Both take the same time from the object point to the image. How much longer is the edge ray’s whole path?
Equal times mean equal n × length summed along each path. The centre ray’s extra 5.0 mm of glass counts as 1.5 × 5.0 = 7.5 mm, so the edge ray needs 7.5 mm more in air; its whole path is 7.5 − 5.0 = 2.5 mm longer (reasoned from NCERT page 261).