Question

The focal length of a lens is the same for lights of all colours. Is the statement true?

Answer 1

According to the lens maker formula we will define the focal length of the lens. The expression is
$\dfrac{1}{f} = \left( {\mu - 1} \right)\left[ {\dfrac{1}{{{R_1}}} - \dfrac{1}{{{R_2}}} + \dfrac{{\left( {\mu - 1} \right)d}}{{\mu {R_1}{R_2}}}} \right]$
Here, f is the focal length,
$\mu$ is the refractive index
$R_1$ and $R_2$ is the radius of the curvature
d is the thickness

Complete answer:
The High frequency waves, like the blue colour, travel the slowest in any medium, compared to the low frequency waves like red colour. Exclude vacuum, because in vacuum they all travel with the same speed.
Consequently, the high frequency waves like blue colour, that bend more because of more refraction or more refractive index, compared to the low frequency waves like red.
Consequently, when an incident on a convex or a concave lens, blue color would bend more and thus converge or diverge closer to the lens. Hence, the blue colour would have a shorter focal length, compared to red colour.
The focal length of a lens depends on their refractive index. The refractive index is different for the lights of different colours, and then the focal length of a lens will be different for different lights of different colors.

So, the statement is False.

Note:
The focal length is that property of the lens and the colour of the light that depends on the wavelength. The focal length of the lens is independent of the colour, wavelength and the frequency of the light which is passing across the lens.
The refraction of the light is depending on the colour. The light with more wavelengths like red refracts the least and the colour with minimum like violet wavelength refracts the maximum.