Question

The refractive indices of flint glass for red and violet lights are 1.613 and 1.632 respectively. Find angular dispersion produced by a thin prism of flint glass having refractive angle \[{{15}^{o}}\].
A. 0.0305
B. 0.0502
C. 0.405
D. 0.285

Answer 1

Hint: Use the expression for deviation of light to calculate the deviations for red and violet lights respectively. Take their difference to find the angular dispersion.

Formula used: $\delta =A\left( n-1 \right)$
$\delta $ is the angle of deviation
$n$ is the refractive index
$A$ is the prism angle

Complete step by step solution:
For red light
\[{{\delta }_{r}}=A\left( {{n}_{r}}-1 \right)={{15}^{o}}\times \left( 1.613-1 \right)={{9.195}^{o}}\]
For violet light
${{\delta }_{v}}=A\left( {{n}_{v}}-1 \right)={{15}^{o}}\times \left( 1.632-1 \right)={{9.48}^{o}}$
Angular dispersion is the angular spread between the two extreme colours. It can be evaluated as
$\text{ }\!\!\Delta\!\!\text{ }\delta ={{\delta }_{v}}-{{\delta }_{r}}={{9.48}^{o}}-{{9.195}^{o}}={{0.285}^{o}}$

The correct answer is option (D)

Additional Information: Dispersion of light is the splitting of white light into seven constituent colours of different wavelengths. When light falls on a thin prism, it gets refracted. The different components of lights have different refractive indices and travel with different speeds. In accordance with Snell’s law, they all emerge with different angles of refraction despite having the same angle of incidence. Red light has the longest wavelength and least refractive index and violet light has the shortest wavelength and largest refractive index. As a result red colour deviates the least and is present at the top of the spectrum whereas violet light deviates the most and is present at the bottom of the spectrum. Rainbows are formed due to the phenomena of dispersion. The water droplets present in the air after rainfall acts as tiny prisms when sunlight passes through them. Dispersion also causes chromatic aberration in lenses.
Flint glass is a combination of silicon dioxide with lead or potassium. It has a high refractive index and high degree of light dispersing power.

Note: A thin prism has a very small refracting angle and consequently a small angle of incidence and angle of refraction. The formula for angle of deviation is derived by using approximations for a thin prism.