Question

For a flint glass refractive index for red, yellow and violet colour of light are 1.613, 1.620 and 1.632 respectively. Find the dispersive power of the material of glass.

Answer 1

Hint: Dispersive power can be defined as the measure of the difference in refraction of light of the highest wavelength and the lowest wavelength when it passes through the given material. Dispersive power (\[\omega \]) can also be expressed in terms of refractive indices. The relation is formulated as given below. refractive index for red, yellow and violet colour of light are given in the question.

Formula used:
\[\omega =\dfrac{{{\mu }_{V}}-{{\mu }_{r}}}{{{\mu }_{Y}}-1}\]

Complete step by step answer:
Dispersive power can be defined as the measure of the difference in refraction of light of the highest wavelength and the lowest wavelength when it passes through the given material. It is expressed in terms of the angles of the two extreme wavelengths. The angle between the two extremes wavelengths increases as dispersive power increases.
Dispersive power (\[\omega \]) can also be expressed in terms of refractive indices. The relation is formulated as
\[\omega =\dfrac{{{\mu }_{V}}-{{\mu }_{r}}}{{{\mu }_{Y}}-1}\]
Where \[\mu \]are the refractive indices of different colours.
In the question refractive index for red, yellow and violet colour of light are given to be 1.613, 1.620 and 1.632 respectively
\[\begin{align}
  & {{\mu }_{r}}=1.613 \\
 & {{\mu }_{Y}}=1.620 \\
 & {{\mu }_{V}}=1.632 \\
\end{align}\]
Plugging in the values in the formula we get
\[\omega =\dfrac{{{\mu }_{V}}-{{\mu }_{r}}}{{{\mu }_{Y}}-1}\]
\[\begin{align}
  & \Rightarrow \omega =\dfrac{1.632-1.613}{1.620-1} \\
 & \Rightarrow \omega =\dfrac{0.019}{0.620} \\
 & \therefore \omega =0.031 \\
\end{align}\]

So, the of the given flint glass is 0.031.

Note:
Dispersion of light is the phenomenon of splitting of white light into its seven constituent colours of different wavelengths and frequencies. When the white light falls on a prism or flint glass, different constituent colours travel at different speeds and thus have different refractive indices. As a result, they come out of the prism with different angles of emergence and thus split or disperse. The order of the dispersed light can be remembered by the acronym VIBGYOR.