Question

Calculate the dispersive power for glass from the given data ${\mu _v} = 1.523$ and ${\mu _r} = 1.5145$
A. $0.0012$
B. $0.2333$
C. $0.1639$
D. $0.9$

Answer 1

Hint: Here we have to use the concept and formula of dispersive power and mean refractive index to get the answer:
The ability of a transparent medium to distinguish various colours of light by refraction, as determined by the difference in refractivity, for two given greatly varying wavelengths separated by the refract at some given intermediate wavelength.

Complete step by step answer:
Dispersive power is the measurement of the potential of the material to scatter light and is proportional to the quotient of the difference in the refractive indices of the material for two representative wavelengths separated by the difference in the refractive index for the intermediate wavelength.
Refractive index: The refractive index measures the bending of a beam of light after passing from one medium to another.
The refractive index n is characterized as the proportion of the sine point of incidence to the sine point of refraction, in the event that i is the angle of incidence of the beam in the vacuum (point between the approaching beam and opposite to the outside of the medium alluded to as normal) and r is the angle of refraction (point between the medium and the normal beams).

The refractive index is given by:
$n = \dfrac{{\sin i}}{{\sin r}}$

Mean refractive index means the average of two or more refractive indices.
$
 \mu = \dfrac{{{\mu _v} + {\mu _r}}}
{2} \\
 = \dfrac{{1.523 + 1.5145}}
{2} \\
 = 1.5192 \\
$

The formula for dispersive power is given by:
$
 w = \dfrac{{{\mu _v} - {\mu _r}}}
{{\mu - 1}} \\
 = \dfrac{{1.523 - 1.5145}}
{{1.5192 - 2}} \\
 = 0.01639 \\
$
The dispersive power for glass is $0.01639$ .

So, the correct answer is “Option C”.

Note:
The dispersive power is free of angle but dependent upon glass material. The mean dispersive power is not given in the question, so we have to calculate the mean dispersive power.
The difference in the refractive indices of the material for two representative wavelengths separated by the difference in the refractive index for the intermediate wavelength.