A person cannot see the objects distinctly, when placed at a distance less than 50 cm. a. Identify the…
A person cannot see the objects distinctly, when placed at a distance less than 50 cm.
a. Identify the defect of vision.
b. Give two reasons for this defect.
c. Calculate the power and nature of the lens he should be using to see clearly the object placed at a distance of 25 cm from his eyes.
d. Draw the ray diagrams for the defective and the corrected eye.
Solution
a. **Hypermetropia (far-sightedness).**
b. Decrease in the power of the eye lens, or shortening of the eye ball.
c. The object is to be placed at $u = -25\ \text{cm}$ and its image must form at his near point, $v = -50\ \text{cm}$.
$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{-50} - \dfrac{1}{-25} = -\dfrac{1}{50} + \dfrac{2}{50} = \dfrac{1}{50}\ \text{cm}^{-1}$
$f = +50\ \text{cm}$
$P = \dfrac{100}{f\ (\text{cm})} = \dfrac{100}{50} = +2\ \text{D}$
He should use a **convex lens of power $+2\ \text{D}$**.
d. Ray diagrams: for the defective eye the image of a nearby object forms **behind** the retina; with the convex lens the rays converge more, bringing the image **onto** the retina.
