question_answer

The power of lens, a short sighted person uses is -2D. Find the maximum distance of an object, which he can see without spectacle.

A)  25 cm                                  

B)  50 cm

C)  100 cm                

D)  10 cm

Correct Answer: B

Solution :

                Power (P) of a lens is inverse of focal length \[(f)\] (in metres). \[\therefore \]  \[P=\frac{1}{f}\] \[\Rightarrow \]               \[f=\frac{1}{P}=-\frac{100}{2}=-50\,cm\] Since, focal length is negative it is a concave lens, from lens formula, we have                 \[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\] where v is image distance, u is object distance. Given, \[v=-25\text{ }cm,\text{ }f=-50\text{ }cm\] \[-\frac{1}{50}=-\frac{1}{25}-\frac{1}{u}\] \[\therefore \] \[\frac{1}{u}=-\frac{1}{25}+\frac{1}{50}=\frac{-2+1}{50}=-\frac{1}{50}\] \[\Rightarrow \] \[u=-\text{ }50\text{ }cm\] \[\therefore \] Object distance is 50 cm.