Question

A fine beam of white light is incident upon the longer side of a plane parallel glass slab of breadth 5 cm at angle of incidence 60°.

Calculate lateral deviation of red and violet rays and lateral dispersion between them as they emerge from the opposite side.

Refractive indices of the glass for red and violet are 1.51 and 1.53 respectively.

Answer 1

As shown in figure,

VM = L_V = lateral deviation for violet colour,

RT = L_R = lateral deviation for red colour,

∴ Lateral dispersion between these colours,

L_VR = L_V – L_R

∴ r_R = sin^-1 (0.5735) ≈ 35°

Similarly,

= antilog {log (1.732) – log (3.06)}

= antilog {0.2385 – 0.4857}

= antilog 11.7528}

= 0.5659

∴ sin r_V = 0.566

∴ r_V = sin^-1 (0.566) = 34°28′

∴ Angle of deviation for red colour

= i – r_R = 60° – 35° = 25°

and that for violet colur = i – r_V = 60° – 34°28′

= 25°32′

From figure, in ∆ANR,

∴ For red colour, L_R = RT = AR [sin(i – r_R)]

= AR [sin (25°)]

= 6.104 × 0.4226

= 2.58 cm

For violet colour, L_V = VM

= AV [sin (i – r_V)]

= AV × sin (25° 32′)

= 6.065 × 0.431

= 2.61 cm

∴ L_VR = L_V – L_R = 2.61 – 2.58 = 0.03 cm

= 0.3 mm