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Chapter 33: Problem 81

You are experimenting with a magnifying glass (consisting of a single converging lens) at a table. You discover that by holding the magnifying glass \(92.0 \mathrm{~mm}\) above your desk, you can form a real image of a light that is directly overhead. If the distance between the light and the table is \(2.35 \mathrm{~m},\) what is the focal length of the lens?

Short Answer

Expert verified
Answer: The focal length of the lens is 0.088 m or 88.0 mm.

Step by step solution

01

Convert the given distances to meters

First, we need to convert the given distances into the same unit, in this case, meters. Object distance, \(d_o = 2.35 \mathrm{~m}\) (already in meters) Image distance, \(d_i = 92.0 \mathrm{~mm} = 0.092 \mathrm{~m}\) (converted from millimeters to meters)
02

Apply the lens equation

Now, we can apply the lens equation to find the focal length \(f\) of the lens: \(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\) Plug in the values of \(d_o\) and \(d_i\) we found in step 1: \(\frac{1}{f} = \frac{1}{2.35} + \frac{1}{0.092}\)
03

Solve the equation for the focal length

Solve the equation for \(f\): \(\frac{1}{f} = \frac{2.35 + 0.092}{2.35 \times 0.092}\) \(f = \frac{2.35 \times 0.092}{2.35 + 0.092}\)
04

Compute the focal length

Now, calculate the value of \(f\): \(f = \frac{2.35 \times 0.092}{2.35 + 0.092} = 0.088 \mathrm{~m}\)
05

Present the focal length

The focal length of the lens is \(0.088 \mathrm{~m}\) or \(88.0 \mathrm{~mm}\).

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