Wave Nature of Light: Hygens' Principle

₁n₂ = v₁/v₂ = 4/3 ≈ 1.33

Step 1: Huygens' principle proves that ₁n₂ = sin i / sin r = v₁/v₂ (speed in first medium / speed in second medium). Step 2: ₁n₂ = v₁/v₂ = (2.0 × 10⁸) / (1.5 × 10⁸) = 2.0/1.5 = 4/3 ≈ 1.33. Step 3: This value (≈1.33) is the refractive index of water with respect to a medium like dense glass — physically meaningful. Step 4: Wrong option B inverts the ratio (that would be ₂n₁). Wrong option D uses c instead of v₁, which would give the absolute refractive index of medium 1 with respect to vacuum, not between the two media.

sin i = BA'/AA' from triangle BAA'

Step 1: In the Huygens' refraction diagram, AA' is the refracting surface. Triangle BAA' has BA' as the perpendicular from B to AA' (the incident wavefront is AB, so BA' ⊥ AA'). Step 2: The angle of incidence i is the angle between the incident ray (normal to AB) and the normal to SS'. In triangle BAA', angle BAA' = i, and sin(BAA') = BA'/AA'. Step 3: Similarly, in triangle AB'A', angle AA'B' = r, so sin r = AB'/AA'. Step 4: Dividing: sin i/sin r = BA'/AB' = v₁t/v₂t = v₁/v₂, giving Snell's law. Wrong option B gives sin r, not sin i. Wrong option C inverts the sine to give cosine-like ratio.

1.875 × 10⁸ m/s

Step 1: The speed of light in a medium is v = c/n, where n is the refractive index. Step 2: v = (3 × 10⁸ m/s) / 1.6 = 1.875 × 10⁸ m/s. Step 3: Note that the frequency (6 × 10¹⁴ Hz) is irrelevant here — it is given as a distractor to test understanding that speed depends only on the medium (refractive index), not on frequency (in this context). Step 4: Wrong option B (4.8 × 10⁸) comes from multiplying c × n instead of dividing. Wrong option C (3.0 × 10⁸) ignores the medium. Wrong option D confuses n with the answer directly.

Spherical converging wavefront; centre travels through thicker glass (slower), so edges emerge first making the wavefront converge

Step 1: A convex lens is thicker at the centre and thinner at the edges. Step 2: Speed of light in glass (v = c/n) is less than in air (n > 1). So light slows down more in thicker regions. Step 3: The central portion of the wavefront spends more time in glass (travels slower there), while the edges spend less time in glass. Step 4: As a result, the edges of the wavefront emerge from the lens before the centre, causing the wavefront to curve inward — forming a spherical converging wavefront. Wrong option B incorrectly states edges are thicker — in a convex lens the centre is thicker. Wrong opti