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 ± 0.2 cm and q = 3.1 ± 0.2 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?

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.Step 2 of 3:

Here the focal length of a lens satisfies .

p= 2.3 0.2 cm , which means p= 2.3 , and the uncertainty .

q = 3.1 0.2 cm , which means q = 3.1 , and the uncertainty .

So the focal length of the lens

f =

=

= 1.320 cm

And

=

=

=

= 0.3295

=

=

=

= 0.1814

So the uncertainty in the estimate is

=

= 0.075

Therefore the estimate of focal length is (1.320 0.075) cm. And the uncertainty in the estimate is 0.075 cm.