Question

A person needs a lens of power minus 5.5 for correcting his distance vision. For correcting his near vision, he needs a lens of power 1.5. What is the focal length of the lens required for correcting distance vision near vision?

a) -0.18 m, 0.67 m
b) -0.33 m, 0.50 m
c) -0.20 m, 0.60 m
d) -0.25 m, 0.75 m

Answer 1

The focal length of the lens required for correcting distance vision near vision is a) -0.18 m, 0.67 m

How to find focal length?

The relationship between focal length (f) and power (P) for a lens is given by the formula:

`\[ P = (1)/(f) \]`

where

P = diopters (measured in
`\(\text{m}^(-1)\)`) and

f = meters.

For distance vision, the person needs a lens with a power (
`\(P_d\)`) of -5.5. So,

`\[ P_d = (1)/(f_d) \]`

For near vision, the person needs a lens with a power (
`\(P_n\)`) of 1.5. So,

`\[ P_n = (1)/(f_n) \]`

Now, find the focal lengths for distance (
`\(f_d\)`) and near (
`\(f_n\)`) vision:

`\[ f_d = (1)/(P_d) = (1)/(-5.5) \]`

`\[ f_n = (1)/(P_n) = (1)/(1.5) \]`

Calculate these values:

`\[ f_d \approx -0.182 \, \text{m} \]`

`\[ f_n \approx 0.667 \, \text{m} \]`

So, the correct answer is:

a) -0.18 m, 0.67 m