question_answer

A person who can see things most clearly at a distance of 10 cm requires spectacles to enable to see clearly things at a distance of 30 cm. What should be the focal length of the spectacles?                 [BHU M-2003]

A)  15 cm (concave)                             

B)  15 cm (convex)

C)  10cm                                   

D)  Zero

Correct Answer: A

Solution :

                 Key Idea: The defect of short-sightedness is removed by using a lens which diverges the rays from object. The person can see near object (10 cm) but cannot see the distant objects distinctly. In order to remove this defect a concave lens of suitable focal length is used which diverges the rays from a distant object reaching the eye such that they appear to be coming from the eye?s        own far point\[P\]. From lens formula \[\frac{1}{f}=\frac{1}{v}-\frac{1}{u}=-\frac{1}{10}-\left( -\frac{1}{30} \right)=-\frac{2}{30}\]                 \[\Rightarrow \]                               \[\frac{1}{f}=-\frac{1}{15}\]                 \[\Rightarrow \]                               \[f=-15\,\,cm\]