Question

A person uses a lens of power $-5D$ for correcting his distant vision, and a lens of power $+1D$ to correct his near vision. What is the focal length of the lens required to correct his a. distant vision b. near vision?

Answer 1

Step 1: a. Given data

Power of the lens $P=-5D$

Step 2: Expression for the focal length of the lens

$f=\frac{1}{P}$

Here $P$ is the power of the lens

Step 3: Calculation for focal length

Substitute $-5D$ for $P$ in the above expression of the power.

$$\begin{gathered} f=\frac{1}{-5D} \\ =-\frac{100cm}{5} \\ =-20cm \end{gathered}$$

Step 4: b. Given Data

Power of the lens $P=+1D$

Step 5: Calculating the focal length,

Substitute $1D$ for $P$ in above expression of focal length

$$\begin{gathered} f=\frac{1}{1D} \\ =\frac{100cm}{1} \\ =100cm \end{gathered}$$

Hence, the required focal length for distant vision is $-20cm$ and for near vision is $100cm$.