Question

A doctor has prescribed a corrective lens of power \[ + 1.5\,{\text{D}}\] to a patient. Find the focal length of the lens in centimeters. Is the prescribed lens diverging or converging?

Answer 1

Hint: Use the formula for the focal length of the lens. This formula gives the relation between the focal length of the lens and the power of the lens. Determine the focal length of the corrective lens using this formula. Convert the unit of the focal length of the lens in centimeters.

Formulae used:
The formula for the focal length of the lens is given by
\[f = \dfrac{1}{P}\] …… (1)
Here, \[f\] is the focal length of the lens and \[P\] is the power of the lens.

Complete step by step answer:
From the question, we can see that the power of the corrective lens prescribed to the patient by the doctor is \[ + 1.5\,{\text{D}}\].
\[P = + 1.5\,{\text{D}}\]
We can determine the focal length of the corrective lens using equation (1).
Substitute \[ + 1.5\,{\text{D}}\] for \[P\] in equation (1).
\[f = \dfrac{1}{{ + 1.5\,{\text{D}}}}\]
\[ \Rightarrow f = 0.67\,{\text{m}}\]
Hence, the focal length of the lens is \[0.67\,{\text{m}}\].

Convert the unit of the focal length of the lens in the SI system of units.
\[f = \left( {0.67\,{\text{m}}} \right)\left( {\dfrac{{{{10}^2}\,{\text{cm}}}}{{1\,{\text{m}}}}} \right)\]
\[ \Rightarrow f = + 67\,{\text{cm}}\]
Hence, the focal length of the corrective lens prescribed by the doctor to the patient is \[ + 67\,{\text{cm}}\].
The focal length of the corrective lens is positive. The focal length of the converging lens is positive.

Hence, the prescribed corrective lens by the doctor is a converging lens.

Note:
The students may assume that the value of the focal length obtained by substituting the value of power of length in equation (1) will be in centimeter. But the diopter is the SI unit of the power of the lens. Hence, the obtained focal length will have the unit meter in the SI system of units. The students should not forget to convert this unit from meter to centimeter.