Question

The near point of a person is 50 cm and the far point is 1.5 cm. The spectacles required for reading purpose and for seeing distant objects are respectively:
(A) +2D, $-\dfrac{2}{3}D$
(B) $+\dfrac{2}{3}D,-2D$
(C) $-2D,+\dfrac{2}{3}D$
(D) $-\dfrac{2}{3}D,2D$

Answer 1

HintWe should know that the lens formula helps us to calculate the image distance. It is also the formula or we can say that the equation gives us a relationship between the focal length, also the distance of the object and even the distance of the image for a lens.

Complete step by step answer
For reading purpose,
u = 50 cm, v = 25 cm
So now we can write that:
$\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$
So, we have to put the values in the above expression to get that:
$\begin{align}
  & \dfrac{1}{25}-\dfrac{1}{50}=\dfrac{1}{f} \\
 & \Rightarrow f=50cm \\
\end{align}$
Now we know that:
P = +2D
Now for seeing the objects which are at a distant we have:
u =1.5 m and v = $\alpha$
So, we can write that:
$\begin{align}
  & \dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f} \\
 & \Rightarrow f=-\dfrac{3}{2}m \\
\end{align}$
So, the value of P is $\dfrac{-2}{3}D$.

So, we can say that the spectacles required for reading purpose and for seeing distant objects are respectively +2D, $-\dfrac{2}{3}D$.

Hence the correct answer is option A.

Note We should know that crystalline lenses are defined as a transparent, biconvex structure in the eye, which is present along the cornea. There are two lenses which are present, they are convex lens and concave lens. The concave lens is thinner at the centre, a convex lens is thicker at the centre.