how many times focal length of lens will be increased in when immersed in water- prove it.
Answers
As already answered by Shashank, the focal length of a mirror remains the same as it works on the principle of reflection and reflection is independent of the medium.
However, in case of a lens, the principle is that of refraction. The refractive index of the material of the lens depends on the medium from which the ray is approaching the lens and that to which if goes after refraction.
When a ray of light in incident on the lens parallel to the principal axis, it gets refracted and meets the principal axis at the focus.
When the lens is immersed in water the refractive index of the lens reduces. If the refractive indices of water and the lens, with respect to air, are, say, [math]1.3333[/math] and [math]1.5,[/math] when the lens is immersed in water, its refractive index with respect to water would be [math]\frac{1.5}{1.3333} = 1.125.[/math]
Since the refractive index is lesser, as compared to not being immersed in water, the ray of light would be deviated to a lesser extent. Hence, the point where the refracted ray would meet the principal axis would be farther away from the lens as compared to not being immersed in water.
[math]\Rightarrow \qquad[/math] The focal length of the lens would be increased when immersed in water.