Question

Find the focal length of a convex lens, if its power is +2.0D.
A. +0.5m
B. -0.5m
C. +1.0m
D. -1.0m

Answer 1

Hint:Power of a lens can be defined somewhat up to the bending or diverging power of any lens. In other words Optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens, mirror or other optical system converges or diverges light.
It can be also defined as reciprocal of the focal length of the device: \[P = \dfrac{1}{f}\] High optical power corresponds to short focal length. The SI unit for optical power is the inverse meter$({m^{ - 1}})$, which is commonly called the diopter.

Complete step by step solution:
Given,
Power of a convex lens = $ + 2.0D$
$\because $We know that power of a lens \[P = \dfrac{1}{f}\] where $P$implies the power of lens and $f$implies the focal length
$\therefore $From the above, we can write,
$\begin{gathered}
  P = \dfrac{1}{f} \\
   \Rightarrow + 2.0 = \dfrac{1}{f} \\
   \Rightarrow f = \dfrac{1}{2} \\
   \Rightarrow f = 0.5m \\
\end{gathered} $
Thus our required answer is $f = + 0.5m$(here + signifies positive focal length of convex lens)


Note:In these types of questions be very careful while handling signs. Always follow the sign conventions and if it asked to find the focal length or some other things related to focal length always cross-check with the type of mirror/lens.