Question

Refractive index of violet, yellow, and red colour of light for a material of lens are 1.66, 1.64 & 1.62 respectively. If the mean focal length of the lens is 10 cm. Then chromatic aberration between the colour of violet and red will be:
A. 0.625 cm
B. 0.125 cm
C. 0.02 cm
D. 0 cm

Answer 1

Hint: Chromatic aberration is an optical defect. Chromatic aberration will cause the splitting of white light into its component colours and the rays of different wavelengths will travel in different paths. Chromatic aberration is the product of dispersive power and focal length of the lens.

Complete step by step answer:
First we can sort the given details from the question.
Refractive index of violet light, \[{{\mu }_{v}}=1.66\]
Refractive index of yellow light, \[{{\mu }_{y}}=1.64\]
Refractive index of red light, \[{{\mu }_{r}}=1.62\]
Mean focal length of the lens, \[f=10\text{ cm}\]
Dispersive power of a material between the violet and red colour can be calculated by
\[\omega =\dfrac{({{\mu }_{r}}-{{\mu }_{v}})}{({{\mu }_{y}}-1)}\]
We can assign the given values to the equation.
\[\omega =\dfrac{(1.66-1.62)}{(1.64-1)}\]
\[\omega =0.0625\]
Chromatic aberration is the product of dispersive power of a lens and focal length of it.
\[\Rightarrow \omega \times f\]
\[\Rightarrow 0.0625\times 10\text{ cm = 0}\text{.625 cm}\]
Therefore the chromatic aberration between the violet and red colour is 0.625 cm.
So, the correct option is A.

Additional information:
Dispersive power does not depend on the shape of the material. However, it depends on the properties of the material. That’s why we are using the same formula for lens as well as prism. It is the ratio of angular dispersion to the angle of deviation for the mean wavelength.
\[\text{Dispersive power = Angular dispersion/Mean deviation}\]
Or we can write like this,
\[\text{Dispersive power = (deviation of violet - deviation of red)/deviation of yellow}\]
Since red and violet are the extreme colours and that can give the angular dispersion.

Note: In the denominator of the dispersive power equation, we are subtracting one from the refractive index of yellow. Since we are calculating the deviation of yellow.
Chromatic aberration is depending upon the materials. More chromatic aberration will produce if we are using a lens of high power. For monochromatic lights, chromatic aberration will not occur.