Question

All the listed things below are made of flint glass which one of these have greatest dispersive power $(\omega )$
a) Prism
b) Glass slab
c) Biconvex lenses
d) All have same $(\omega )$

Answer 1

Hint: In order to solve the question, we will compare the dispersive power of all the mediums. The dispersive power of any transparent material is determined by the ratio of the difference in refractive index of two different wavelengths to the refractive index at some predetermined intermediate wavelength.
Formula required to solve the question
Dispersive power of glass = $\dfrac{{{\mu _v} - {\mu _r}}}{{{\mu _y} - 1}}$
${\mu _{red}}$= Refractive index of red
${\mu _{yellow}}$ = Refractive index of yellow
${\mu _{violet}}$ = Refractive index of violet

Complete answer:
Flint glass is made up of silicon dioxide (SiO$_2$) and potassium or lead. When compared to other forms of glass, it has a comparatively high refractive index and a high degree of light dispersing capacity. Dispersion is the process of breaking down white light into its constituent colours. A colour spectrum is a grouping of colours. The dispersive power of a transparent medium is the ability to separate different colours of light by refraction.
Refractive index of red,${\mu _{red}}$ = 1.60
Refractive index of yellow,${\mu _{yellow}}$ = 1.61
Refractive index of violet,${\mu _{violet}}$ = 1.62
Substituting the value of refractive index of red, yellow and violet in the formula of dispersive power
Dispersive power of glass = $\dfrac{{{\mu _v} - {\mu _r}}}{{{\mu _y} - 1}}$
$ \Rightarrow \dfrac{{1.62 - 1.60}}{{1.61 - 1}}$
= 0.033
For prism, glass slab and biconvex lenses all of them are made of the same material and dispersion of red, yellow, violet so the dispersive power is same.

Hence, the correct option is d) All have same $(\omega )$

Note:
Keep in mind that violet rays have a higher deviation and refractive index than red rays. As a result, violet light travels slower through glass than red rays. As mean values, the refractive index and deviation of yellow rays are used.