Question

A man is unable to see closer than 1 m clearly. The power of lenses of his spectacles should be to see nearby objects.
A. 3 D
B. 6 D
C. 1 D
D. 2 D

Answer 1

Hint: The distance of distinct vision for the normal person is 25 cm. Use the lens formula to determine the focal length of the lens used by the person. The power of the lens is the reciprocal of the focal length.


Formula used:
\[\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}\]
Here, f is the focal length, v is the object distance and u is the image distance.

Complete step by step answer:
We have to determine the focal length of the lens that he should use using the lens formula below,\[\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}\]

Here, f is the focal length, v is the object distance and u is the image distance.

We have given that the person unable to see object closer than 1 m, therefore, the object distance is
\[ - 1\,m = - 100\,cm\].

The image distance is the distance of distinct vision of the normal person, therefore, \[u = - 25\,cm\].

Substitute \[ - 100\,cm\] for v and \[ - 25\,cm\] for u in the equation of lens formula.
\[\dfrac{1}{f} = \dfrac{1}{{ - 100}} - \dfrac{1}{{ - 25}}\]
\[ \Rightarrow \dfrac{1}{f} = \dfrac{3}{{100}}\,cm\]
\[\therefore f = \dfrac{{100}}{3}\,cm = \dfrac{1}{3}\,m\]

We know that the power of the lens is reciprocal of the focal length. Therefore,
\[P = \dfrac{1}{f}\]

Substitute \[\dfrac{1}{3}\,m\] for f in the above equation.
 \[P = \dfrac{1}{{\left( {\dfrac{1}{3}} \right)\,m}}\]
\[\therefore P = 3\,D\]

So, the correct answer is option (A).

Note:While using the formula for the power of the lens, the unit of focal length should be in meters. If you got the focal length in cm, convert it into m. Also, the dioptre is the unit of power of the lens which is inverse of the meter.