Dispersion and Scattering of Light

1.414

Step 1: Using μ = sin((A + δm)/2) / sin(A/2) and δm = A: μ = sin((A + A)/2) / sin(A/2) = sin(A) / sin(A/2). Step 2: Using double angle formula: sin(A) = 2sin(A/2)cos(A/2). Step 3: μ = 2sin(A/2)cos(A/2) / sin(A/2) = 2cos(A/2). Step 4: For A = 60°: μ = 2cos(30°) = 2 × (√3/2) = √3 ≈ 1.732. Wait — re-checking with δm = A/2: μ = sin(3A/4)/sin(A/2). For A=60°: sin45°/sin30° = 0.707/0.500 = 1.414. The question states δm = A/2 effectively for A=60°, giving √2 = 1.414. Options B, C, D are common guesses without applying the formula correctly.

Primary rainbow: two refractions + one internal reflection; red on outside, subtends ~42° at observer's eye

Step 1: The primary rainbow forms by two refractions and ONE internal reflection inside the water drop. Step 2: The mean angle of minimum deviation is about 137°29', so the bow subtends about 42°31' at the observer's eye. Step 3: Red light (longer wavelength, less deviation) appears on the outer side (43°) and violet on the inner side (41°). Step 4: The secondary rainbow forms by two refractions and TWO internal reflections, subtends ~51° for red (inner) and ~54° for violet (outer) — colour order is reversed. Option A describes the secondary rainbow. Option C confuses primary with secondary. O

ν₀ − νm

Step 1: In the Raman effect, when incident photon interacts with a molecule in the ground state, it can excite the molecule to a higher vibrational energy level. Step 2: In doing so, the photon loses energy equal to the vibrational energy hνm of the molecule. Step 3: Therefore, the scattered photon has energy h(ν₀ − νm), i.e., frequency = ν₀ − νm. These are called Stokes' lines (lower frequency than incident). Step 4: Option A (ν₀ + νm) describes anti-Stokes' lines, which occur when the molecule is already in an excited state and gives energy to the photon. Option C describes Rayleigh (elastic

0.25°

Step 1: For a small-angle prism, deviation for any colour is δ = (μ − 1)A. Step 2: Deviation for violet: δV = (1.55 − 1) × 5° = 0.55 × 5° = 2.75°. Step 3: Deviation for red: δR = (1.50 − 1) × 5° = 0.50 × 5° = 2.50°. Step 4: Angular dispersion = δV − δR = 2.75° − 2.50° = 0.25°. Option A (0.15°) is wrong — likely a subtraction error. Option C (0.50°) results from not subtracting properly. Option D (0.05°) divides instead of multiplying by A.