Question

You ordered a converging lens of focal length 3 m but the company delivered a lens whose focal length was only 1 m. You do not have time to wait for a replacement so you decide to correct the problem by placing a diverging lens next to the lens they sent you. What must the focal length be for this diverging lens?

Answer 1

Answer on Question #71615, Physics / Optics

Question. You ordered a converging lens of focal length $3m$ but the company delivered a lens whose focal length was only $1m$. You do not have time to wait for a replacement so you decide to correct the problem by placing a diverging lens next to the lens they sent you. What must the focal length be for this diverging lens?

Given.

$$f = 3m; f_1 = 1m.$$

Find.

$$f_2 = ?.$$

Solution.

If two thin lenses are separated in air by some distance $d$, the focal length for the combined system is given by

$$\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} - \frac{d}{f_1 f_2}.$$

Consider the simplest case where lenses are placed in contact ($d = 0$). Then

$$\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} \rightarrow \frac{1}{3} = \frac{1}{1} + \frac{1}{f_2} \rightarrow f_2 = -1.5m$$

Answer. $f_2 = -1.5m$.

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