Question

You are asked to experimentally determine the focal length of a converging lens.

(a) Your teacher first asks you to estimate the focal length by using a distant tree visible through the laboratory window. Explain how you will estimate the focal length.

To verify the value of the focal length, you are to measure several object distances so and image distances s_i using equipment that can be set up on a tabletop in the laboratory.

(b) In addition to the lens, which of the following equipment would you use to obtain the data?

____Lighted candle ____ Candleholder ____ Desk lamp ____ Plane mirror ____ Vernier caliper ____ Meterstick ____ Ruler ____ Lens holder ____ Stopwatch ____ Screen ____ Diffraction grating

(c) On the tabletop below, sketch the setup used to obtain the data, labeling the lens, the distances so and s_i and the equipment checked in part (b).

You are to determine the focal length using a linear graph of 1/s_i versus 1/s_o. Assume that you obtain the following data for object distance so and image distance s_i.

(d) On the grid below, plot the points in the last two columns of the table above and draw a best-fit line through the points.

(e) Calculate the focal length from the best-fit line.

Answer 1

(a) Estimate the focal length by focusing the image of the tree on a screen, the distance between the image and the lens is the focal length since the distant rays are assumed horizontal.

(b)

(c)

(d)

(e) From the equation … 1/f = 1/d_o + 1/d_i = 1/f = 1/s_o + 1/s_i … we rearrange this equation to be of the form y = mx + b

Y = mx + b (1/s_i) = (1/s_i) + (1/f) 

So the 1/f is the y intercept from the graph 3.3 = 1/f → f = 0.3

Or you could pick a point on the line and plug in for 1/s_i and 1/so to solve for 1/f