Question

A person who can see things most clearly at a distance of 10 m, requires spectacles to enable to see things clearly at a distance of 30 m. What should be the focal length of the spectacles?
A. 15 m
B. $- 15\,{\text{m}}$
C. 10 m
D. Zero

Answer 1

Find out what type of lens the person should use. Use the lens equation to determine the focal length of the lens.

Formula used:
$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}$

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

Complete step by step answer: Since the person cannot see the objects placed at a distance 30 m clearly and requires spectacles to see these objects at 10 m, the image of the object should be formed on the same side of the object. Thus, the person must use a spectacle made up of concave lenses.

We use the lens formula to determine the focal length of the spectacle as follows,
$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}$

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

Since the lens used is a concave lens, the image distance and object distance both are negative. Therefore, substitute $- 10\,m$ for v and $- 30\,m$ for u in the above equation.
$\dfrac{1}{f} = \dfrac{1}{{ - 10}} - \dfrac{1}{{ - 30}}$
$\Rightarrow \dfrac{1}{f} = - \dfrac{1}{{15}}$
$\Rightarrow f = - 15\,m$

The negative sign in the above equation implies that the spectacle is concave.

So, the correct answer is option (B).

Note: Always fix the coordinates for measurement of image distance and object distance. If the object and image is on the same side of the lens, then the distance from the lens is negative and the lens is said to concave the lens. For a convex lens, the image of the object is on the opposite side of the lens, therefore, the image distance is positive and object distance is negative.