Question

The refractive index of flint glass for blue F line is 1.6333 and red C line is 1.6161. If the refractive index for yellow D line is 1.622, the dispersive power of glass is:
A. 0.0276
B. 0.276
C. 2.76
D. 0.106

Answer 1

Hint: Light consists of seven colors which are collectively known as VIBGYOR. According to Cauchy, different colors have different refractive index for a particular material. This is the reason why if the light is passed through a prism, it splits into various colors. The dispersive power is a unique property of a medium which depends only upon the material and not on its geometry. It is denoted by ($\omega$). It is the measure of how much a medium can split light into different colors.

Formula used:
$\omega = \dfrac{\mu_V - \mu_R}{\mu_Y -1}$, where $\mu$ is the refractive index of the medium for a particular color.

Complete answer:
According to Cauchy’s equation, the refractive index and the wavelengths are inversely related. Hence if the wavelength of the wave is increased, its refractive will decrease for that wave. Hence speed, which is directly related to the wavelength also increases. Thus, light with maximum wavelength will have maximum velocity whereas light with minimum wavelength will have minimum velocity in a particular medium. Hence there must be some property of the medium which defines the phenomenon. This property is called dispersive power.
Now, given $\mu_R = 1.6161,\ \mu_V = 1.6333,\ \mu_Y = 1.622$
Putting these values in equation $\omega = \dfrac{\mu_V - \mu_R}{\mu_Y -1}$, we get
$\omega= \dfrac{1.6333 - 1.6161}{1.622 - 1} = 0.276$

Hence option A. is correct.

Note:
We use the refractive index of yellow color as the mean refractive index. Students usually think that the mean refractive index is of green color as it lies in the centre of VIBGYOR. But we must realize that this mean relation is not linear. After actual calculation, we get a mean refractive index that comes out to be approximately equal to the yellow color refractive index.