A person needs a lens of power, -5.5 dioptres for correcting his distant vision. For correcting his near vision, he needs a lens of power +1.5 dioptres. What is the focal length of the lens required for correcting (i) distant vision, and (ii) near vision?

Question

Philoid · Accepted Answer

(i) For distant vision:

Power of lens, P = -5.5 D

$Power (in D) = \frac{1}{f(m)}$

$\Rightarrow f = \frac{100}{-5.5} = -18.8 cm$

Thus, the focal length of the lens required for correcting distant vision is, -18.2 cm.
Note: The negative sign of the length tells us that it is a concave lens.

(ii) For near vision:

Power of lens, P = + 1.5 D

$Power (in D) = \frac{1}{f(m)}$

$\Rightarrow f = \frac{100 cm}{1.5} = 66.66 cm$

So, Focal length, f = + 66.66 cm (or + 66.7 cm)

Thus, the focal length of the lens required for correcting near vision is + 66.7 cm.

Note: The positive sign of focal length tells us that it is a convex lens.

A person needs a lens of power, -5.5 dioptres for correcting his distant vision. For correcting his near vision, he needs a lens of power +1.5 dioptres. What is the focal length of the lens required for correcting(i) distant vision, and(ii) near vision?

A person needs a lens of power, -5.5 dioptres for correcting his distant vision. For correcting his near vision, he needs a lens of power +1.5 dioptres. What is the focal length of the lens required for correcting

(i) distant vision, and

(ii) near vision?