Refraction and Dispersion of Light through a Prism

Violet

Step 1: Dispersion occurs because different colours of light have different speeds in glass, giving different refractive indices. Step 2: Violet light has the shortest wavelength and travels slowest in glass, so it has the highest refractive index (nV is largest). Step 3: Since deviation δ = (n − 1)A for a thin prism, higher refractive index means more deviation. Step 4: Violet light bends the most towards the base. Red light (longest wavelength) has the lowest refractive index and is deviated the least. Green and Yellow are intermediate colours.

ω = (nV − nR) / (nY − 1)

Step 1: Dispersive power is the ratio of angular dispersion to mean deviation. Step 2: Angular dispersion = δV − δR = (nV − nR) × A (for thin prism). Step 3: Mean deviation (for yellow ray) = δY = (nY − 1) × A. Step 4: So ω = [(nV − nR) × A] / [(nY − 1) × A] = (nV − nR) / (nY − 1). The angle A cancels, showing dispersive power depends only on the material. Option B uses a sum instead of difference. Option C multiplies instead of dividing. Option D uses nY instead of (nY − 1).

0.169

Step 1: Use ω = (nV − nR) / (nY − 1). Step 2: Numerator = nV − nR = 1.62 − 1.52 = 0.10. Step 3: Denominator = nY − 1 = 1.59 − 1 = 0.59. Step 4: ω = 0.10 / 0.59 ≈ 0.169. Option B (0.059) incorrectly uses (nV − nR) in denominator. Option C (0.250) is an over-estimate. Option D (0.100) only calculates the numerator without dividing.

Violet

Step 1: The primary rainbow is formed by sunlight undergoing one total internal reflection and two refractions inside raindrops. Step 2: Red light reaches the observer at a semi-vertical angle of 43° from the line SE produced, while violet light reaches at 41°. Step 3: Since the red rays make a larger angle, they appear on the OUTER edge (top arc). Step 4: Violet rays, making a smaller angle, appear on the INNER edge (bottom arc). This is the reverse of the secondary rainbow. Option A (Red) is the outer edge of the primary rainbow.