Question

Doctor has prescribed a lens having power of +1.5 D. what would be the focal length of the lens? What is the type of lens and what must be the defect in his vision.?

Answer 1

Hint: Since, the prescribed lenses have their power positive these are convex lenses. A convex lens has a positive focal length and since power is described as inverse of focal length taken in metres, thus convex lenses have positive focal length. On the other hand, concave lenses have negative focal length, also, the convex lenses are converging lenses.

Complete step by step solution:
The power of the lens is +1.5 D. so the focal length can be given as
\[\begin{align}
  & f=\dfrac{1}{P} \\
 & \Rightarrow f=\dfrac{1}{1.5} \\
 & \Rightarrow f=0.66m \\
\end{align}\]
We know for myopia or short sightedness concave lenses are used and for hypermetropia or far sightedness convex lenses are used. Since, here convex lens is being used so, the person is suffering from hypermetropia.

Additional Information:
Near-sightedness tends to run in families. Faraway objects appear blurry. The condition may develop gradually or rapidly. To treat such conditions, Treatment options include glasses, contact lenses and surgery such as LASIK

Note:
Since the person is suffering from hypermetropia, the image is formed beyond the retina and not on the retina. When the convex lens is used, they converge the incoming light rays on to the retina and thus he is able to see the objects distinctly. While finding out the power of any lens, the focal length is always to be taken in units of metre. Then only power comes out to be in diopters.