Question

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 dioptre. What is the focal length of the lens required for correcting (i) distant vision, and (ii) near vision?

Answer 1

Answer:

(i). -0.1818 m

(ii). 0.66 m

Explanation:

(i).

Power of the lens for correcting the distant vision = -5.5 Dioptres

Power of the lens for correcting the near vision = +1.5 Dioptres

Now,

We know that the Power of the lens is given by,

$Power, P=\frac{1}{f}\\-5.5=\frac{1}{f}\\f=-0.1818\,m$

Therefore, the Focal length of the lens is given by,

Focal length, f = -0.1818 m

(ii).

The Power of lens for near vision = +1.5 Dioptres

So,

The focal length of the lens is given by,

$f=\frac{1}{P}\\f=\frac{1}{1.5}\\f=0.66\,m$

Therefore, the Focal length of the lens is given by,

Focal length, f = 0.66 m

Answer 2

Answer:

(i). -0.1818 m

(ii). 0.66 m

Explanation:

(i).

Power of the lens for correcting the distant vision = -5.5 Dioptres

Power of the lens for correcting the near vision = +1.5 Dioptres

Now,

We know that the Power of the lens is given by,

Power, P=\frac{1}{f}\\-5.5=\frac{1}{f}\\f=-0.1818\,m

Therefore, the Focal length of the lens is given by,

Focal length, f = -0.1818 m

(ii).

The Power of lens for near vision = +1.5 Dioptres

So,

The focal length of the lens is given by,

f=\frac{1}{P}\\f=\frac{1}{1.5}\\f=0.66\,m

Therefore, the Focal length of the lens is given by,

Focal length, f = 0.66 m