Question

What is the long sightedness? The near point of the long sighted person is at $100cm$ from his eyes. What would be the power of the lens to be used by him in order to read a book placed at $25cm$ from his eyes?

Answer 1

Hint:The human eye has ability to accommodate which allows it to view focused images of both nearby and distant objects. But due to inability of the eye to provide variation of the focal length of the eye lens it loses its ability to focus the nearby object. This inability is called long-sightedness.

Complete step-by-step solution:
Long-sightedness is the inability of the eye to focus on an object which is kept near the eye. It is also called hyperopia. In long-sightedness there is no difficulty to focus on the object which is kept at a long distance. The ability to view nearby objects requires a different lens shape and as we know that the focal length of the eye depends on the aperture of the eye - a shape that the farsighted eye is unable to assume. Subsequently, the Long-sightedness eye is unable to focus on nearby objects. Due to inability to accommodate the eye can no longer assume the high curvature that is required to view nearby objects. The lens' power to refract light has diminished and the images of nearby objects are focused at a location behind the retina.
The given near point of the eye is $100cm$
Distance of the book from eye is $25cm$
To make the book clearly visible to the eye the image of the book must be formed at the near point.
Using lens formula,
$\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$
The power of the lens $P=\dfrac{1}{f}$
$\begin{align}
  & \dfrac{1}{f}=\left( \dfrac{1}{-100}-\dfrac{1}{-25} \right)\dfrac{1}{cm} \\
 & =\left( \dfrac{-1+4}{100} \right)\dfrac{1}{cm} \\
 & =\dfrac{3}{100cm} \\
\end{align}$
Hence, the power of the lens is $P=\dfrac{3}{100}\times 100D=+3D.$

Note:Always not that when substituting the values in the formula
The focal length of the concave lens is negative.
The focal length of the convex lens is positive.