Question

A nearsighted man can clearly see objects up to a distance of 2m. Calculate the power of the lens of the spectacles necessary for the remedy of this defect.

Answer 1

Myopia:

1. Nearsighted or Myopia is a common vision condition in which we can see near objects clearly, but objects farther away are blurry.
2. When the focal length of the human eye is reduced for some reason, then myopia occurs.
3. In this case, the human eye can't focus on far objects.
4. To recover from this defect a concave lens is used.

Power of a lens:

1. The power of a lens is the reciprocal of its focal length.

Step1: Given data

1. The image distance of the lens is $v=2m.$

Step2: Formula used

1. Power of a lens, $P=\frac{1}{f}$, where, f is the focal length of the lens.
2. Focal length of a lens , $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$, where, f is the focal length, v is the image distance and u is the object distance.

Step3: Diagram

Step4: Calculate the power

The man will recover from Myopia when he sees all objects at any distance, i,e. the range of the object distance is infinity, $u=\infty$.

Now, the power of the lens is necessary for the remedy of Myopia is

$$\begin{gathered} P=\frac{1}{f}=\frac{1}{v}+\frac{1}{\infty }=\frac{1}{2}+0\left(\sin ce,\frac{1}{\infty }=0\right) \\ orP=0.5D. \end{gathered}$$

Hence, the power of the concave lens of the spectacles necessary for the remedy of this defect is $0.5D.$