Question

A thin lens has a focal length of -50 cm. What is the power of the lens and what is its nature.

Answer 1

Hint: The formula for power of lens should be used. In the formula the focal length should always be in units of meter, so the units should be taken care of. Substitute the value of focal length in the formula and we will get the power. The sign of power tells about the nature of a lens.

Formula used:
\[Power=\dfrac{1}{f}\]

Complete answer:
The ability to bend a light is called power of a lens. The more will be the power of lens the more will it will refract. The converging ability is called power for convex lens and the diverging ability is called power for concave lens. Power and focal length of a lens are inversely proportional.
So to find the power of a lens, the given formula is used.
\[\begin{align}
  & P=\dfrac{1}{f} \\
 & P=\dfrac{1}{-50\times {{10}^{-2}}} \\
 & P=-2Diopter \\
\end{align}\]
As we see that the power of the lens comes out to be negative. Therefore, it is a concave lens.

Additional Information:
Focal length of the concave lens is negative because the image formed is behind the lens. While for a convex lens the focal length is taken positive because image is formed before the lens. The focal length of concave is in the negative x-direction and for convex lens it is in positive x-direction.

Note:
Lens is an optical device having two surfaces. Parallel incident rays fall on the surface. If the ray converges it is called converging lens and if the ray diverges then it is called diverging lens. The power of the lens depends on the focal length of the lens. Convex lens has positive power whereas a concave lens has negative power.