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Chapter 2: Problem 123

A diverging lens has a focal length of \(20 \mathrm{cm} .\) What is the power of the lens in diopters?

Short Answer

Expert verified
The power of the diverging lens with a focal length of \(20 cm\) is -5 diopters.

Step by step solution

01

Convert the focal length to meters

We have the focal length f in centimeters: \(f = 20\) cm. To convert this to meters, we will use the following conversion: 1 meter = 100 centimeters Thus, \(f = 20 cm \cdot \frac{1 m}{100 cm} = 0.2 m\) Now the focal length in meters is \(f = -0.2\) m (negative because it's a diverging lens).
02

Calculate the power of the lens

Now that we have the focal length in meters, we can use the formula for lens power: Power (P) = 1 / focal length (f) Plugging in the focal length from Step 1: \(P = \frac{1}{-0.2 m} = -5 \mathrm{D}\) So the power of the diverging lens is -5 diopters.

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