Question

The near point of a hypermetropic eye is 1m. Assume that the near point of the normal eye is 25cm. The power of the lens required to correct this defect will be _________ (+3, -3) dioptre.

Answer 1

Hint: We have given the near point of the hypermetropic eye is 1m. Assume that the near point of the normal eye is 25cm. We have to calculate the power.
We know the power; the power is the reciprocal of the focal length. Its SI unit is Dioptre.
The expression for power:
$\text{Power} = \left( {\dfrac{1}{{focal\;length}}} \right) $
$P = \left( {\dfrac{1}{f}} \right) $
But, the focal length is in meters.

Complete step by step solution:
We need the lens to correct the defect. Means Power, But first we have to find the focal length.
We calculate the focal length with the help of lens formula.
The lens formula gives us the relation between object distance (u), image distance (v), and the focal length (f). So, the expression of their relation is
\[\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}\]
We calculate the focal length is in meters. So we change the object distance to meter.
Here, the case of convex lens, image distance and object distance is in negative side, the focal length is in positive side
Object distance, u is 25cm = -0.25m
Image distance, v is = -1m
$\dfrac{1}{f} = \left[ {\left( {\dfrac{1}{{\left( { - 1} \right)}}} \right) - \left( {\dfrac{1}{{\left( { - 0.25} \right)}}} \right)} \right] $
 $\Rightarrow \dfrac{1}{f} = \left[ { - 1 + \dfrac{1}{{0.25}}} \right] $
  $ \Rightarrow \dfrac{1}{f} = \left[ {\dfrac{{ - 0.25 + 1}}{{0.25}}} \right] $
  $ \Rightarrow \dfrac{1}{f} = \left[ {\dfrac{{0.75}}{{0.25}}} \right]$
  $ \Rightarrow f = \left[ {\dfrac{{0.25}}{{0.75}}} \right] $
   $\Rightarrow f = \left[ {\dfrac{{25}}{{75}}} \right]m $
Now, we calculate the power of the lens.
$P = \dfrac{1}{f} $
$\Rightarrow P = \left[ {\dfrac{1}{{\dfrac{{25}}{{75}}}}} \right]$
 $\Rightarrow P = \left[ {\dfrac{{75}}{{25}}} \right] $
 $\Rightarrow P = 3D $
The power of the lens required to correct this defect will be 3Dioptre.

Note: We correct hypermetropic eyes with the help of the convex lens. The convex lens is the converging lens. The hypermetropic is caused due to the cause of the small eyeballs. So, the person requires the convex lens spectacles. The hypermetropic can easily be corrected by the Optometrist.
In front of the hypermetropic eye, moving the image is forward and focuses it correctly on the retina.