Question

If the power of the lens is negative, does it mean that the nature of the lens is diverging?

Answer 1

Hint: In order to solve this question, we should know that there are only two natures of an optical lens either converging or diverging. A converging lens is one which converges the parallel rays of light coming from infinity to the other side of lens after passing though it and a diverging lens is one which diverges the parallel rays of light coming through infinity after passing through the lens.

Complete answer:
 In an optical lens, the focus is the point where the parallel rays of light coming from infinity either converge or diverge depending upon the nature of the lens after passing through the lens. So, this point is known as focus and distance between lens centre and focus point is called focal length.

Power $P$ of a lens is defined as reciprocal of focal length ‘f’ written as $P = \dfrac{1}{f}$ so, if the focal length is negative then power is also negative.And according to sign conventions, the distance measured left to the lens are negative and such lenses which have the diverging nature, their focus lies on the left of the lens so, focal length of diverging lenses are negative so their power also becomes negative.

Hence, yes, if the power of a lens is negative then the nature of the lens will be diverging.

Note: It should be remembered that, most common examples of diverging lenses are concave lenses whose focal length is negative whereas the converging lenses are convex lenses and Power is measured in standard units called Dioptre.