Question

If $\omega$ is the dispersive power and $f$ is the mean focal length, then what is the longitudinal chromatic aberration?
A. $\dfrac{\omega }{f}$
B. $\omega f$
C. $\dfrac{\omega f}{2}$
D. $2\omega f$

Answer 1

Hint: Longitudinal chromatic aberration occurs, when a lens cannot focus different colours in the same focal plane. In longitudinal aberration, the focus of different colours lies at different points in the longitudinal direction along the optical axis.

Complete answer:
Chromatic aberration is defined as failure of an optical lens to focus different wavelengths of light to the same point. It is caused by dispersion.
Dispersion is a phenomenon in which the phase velocity of a wave depends on its frequency. Rainbow is a beautiful result of dispersion. Due to dispersion, the refractive index for every wavelength is different. Since, white light consists of seven colours viz. violet, indigo, blue, yellow, green, orange, and red; which are of different wavelengths. Refractive index for these colours is also different. That is why they converge at different points and cause longitudinal chromatic aberration.
Refractive index of any medium or material is inversely proportional to wavelength of light passing through it.
$\mu \propto \dfrac{1}{\lambda }$
Mathematically, we can define longitudinal chromatic as a product of the dispersion power and the mean focal length of the lens. i.e.
$c=\omega f$

So, the correct answer is “Option B”.

Additional Information:
In an optical lens, the edges of the lens deviate the light more, compared to the centre and thus, act as a prism causing dispersion of light. Dispersion of light is the phenomenon of splitting of white light in its constituent colours.

Note:
Chromatic aberration is defined as failure of an optical lens to focus different wavelengths of light to the same point. It is caused by dispersion.
Refractive index of any medium or material is inversely proportional to wavelength of light passing through it.