Question

To determine the focal length f of a converging thin lens, you place a 4.00- mm-tall object a distance s to the left of the lens and measure the height h ′ of the real image that is formed to the right of the lens. You repeat this process for several values of s that produce a real image. After graphing your results as 1/h′ versus s, both in cm, you find that they lie close to a straight line that has slope 0.208 cm−2 . What is the focal length of the lens?

Answer 1

The focal length of the converging lens is approximately \(4.81 \, \text{cm}\).

The lens formula relates the object distance (\(s\)), image distance (\(s'\)), and focal length (\(f\)) of a lens:

\[ \frac{1}{f} = \frac{1}{s} + \frac{1}{s'} \]

From the given information, you've plotted a graph of \(1/h'\) versus \(s\), and the slope of this graph is related to the focal length.

The slope (\(m\)) is given as 0.208 cm\(^{-2}\). For a converging lens, the focal length is positive. The relation between slope and focal length is given by:

\[ m = \frac{1}{f} \]

Therefore, solving for \(f\):

\[ f = \frac{1}{m} \]

Substitute the given slope:

\[ f = \frac{1}{0.208 \, \text{cm}^{-2}} \]

Calculate:

\[ f \approx 4.81 \, \text{cm} \]

So, the focal length of the converging lens is approximately \(4.81 \, \text{cm}\).