The lens equation says that if an object is placed at a distance \(p\) from a lens, and an image is formed at a distance \(q\) from the lens, then the focal length \(f\) satisfies the equation 1/f = 1/p + 1/q. Assume that \(p=2.3\pm0.2\mathrm{\ cm}\) and \(q=3.1\pm0.2\mathrm{\ cm}\).

a. Estimate \(f\) , and find the uncertainty in the estimate.

b. Which would provide a greater reduction in the uncertainty in \(f\) : reducing the uncertainty in \(p\) to 0.1 cm or reducing the uncertainty in \(q\) to 0.1 cm?

Equation Transcription:

Text Transcription:

p

q

f

p = 2.3 pm 0.2 cm

q = 3.1 pm 0.2 cm

Solution:

Step 1 of 3:

By lens equation the focal length of a lens satisfies the equation = . where p is the difference between the object and the lens and q is the difference between the lens and the image.

If P= 2.3 cm and q= 3.1 0.2 cm we have to find :

- The estimate of focal length f. And the uncertainty in the estimate.
- Which would provides a greater reduction in the uncertainty in f: reducing the uncertainty in p to 0.1 cm or reducing the uncertainty in q to 0.1 cm.