A person needs a lens of power –5.5 diopters for correcting his distant vision. For correcting his near vision, he needs a lens of power +1.5 diopters. What is the focal length of the lens required for correcting:

(i) Distant vision

(ii) Near vision?

a) For distant vision,

Power of lens, $\mathrm{P} =–5.5 \mathrm{D}$

The power $\mathrm{P}$ of a lens of focal length $\mathrm{f}$ is given by the relation,

                                                                          $\mathrm{P} =\frac{1}{\mathrm{f}}$

Thus focal lens of the lens will be, 

                                                                         $\mathrm{f} =\frac{1}{\mathrm{P}}$

Substituting the values in the above equation,

                                                                       $\mathrm{f} =\frac{ 1}{-5.5}$

On simplification ,

                                                                       $\mathrm{f}=-0.181 \mathrm{m}$

Thus, the focal length of the lens for correcting distant vision is $-0.181 \mathrm{m}$.