Question

The focal length of a lens depends on:
A. color of light
B. radius of curvature of the lens
C. material of the lens
D. all of the above

Answer 1

Hint: For different wavelengths of light, the point of convergence i.e. the point of the ray focusing is different, so focal length changes for different colors of light ray and hence the focal length of the lens depends upon the color of the light.
Also, we have to remember the formula for focal length of lens, which is $\dfrac{1}{f} = \left( {\mu - 1} \right)\left( {\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}}} \right),$ this formula tells about refractive index, which is materialistic property. In this formula ${R_1}$ and ${R_2}$ are the radius of curvature of the lens of two sides. Hence the dependency of focal length should be also on the radius of curvature.

Complete step by step answer:
The focal length of a lens depends on the color of light because of changing the color the wavelength is changed and hence the change into the point of convergence has appeared. This appearance of change in point of convergence changes the position of the focal point. So the focal length depends upon the color of light.
Now, by the lens maker formula which is, $\dfrac{1}{f} = \left( {\mu - 1} \right)\left( {\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}}} \right),$where ${R_1},{R_2}$ are radius of curvature of the two sides of the lens, hence focal length of the lens also depends upon the radius of curvature of the lens used.
Here, $\mu $ is the refractive index of the material of which the lens is made, hence the focal length also depends upon the material of the lens.

Hence, option (D) is correct.

Note: When the light rays passing through a lens are focused at different points, depending upon their wavelengths. This phenomenon is known as chromatic aberration. So, this phenomenon tells that for different colors of light ray the focal point is different hence focal length will be also different.