Question

Position of lens (cm)	Position of screen (cm)
1	23.8	70.0
2	45.6	70.0
3	23.1	72.0
4	48.6	72.0
5	22.3	75.0
6	52.2	75.0
7	21.9	77.0
8	54.7	77.0
9	21.7	79.0
10	56.9	79.0

p = object distance, (distance from the bulb to the lens)

q = image distance, (distance from the lens to the screen)

Plot a graph of q versus p for the lens.

Using the asymptotes, determine the two values for f on the graph. If they differ, average the values to find f for the lens. (Please demonstrate in detail how exactly to find asymptotes, and how to determine two values for f on the graph using them).   

Answer 1

position of lens, p in cm	position of screen in cm	image distance q in cm
23.8	70	46.2
45.6	70	24.4
23.1	72	48.9
48.6	72	23.4
22.3	75	52.7
52.2	75	22.8
21.9	77	55.1
54.7	77	22.3
21.7	79	57.3
56.9	79	22.1

from the graph,

focal length, f1 = OA/2 = 33/2 = 16.5 cm

focal length, f2 = OB/2 = 32.5/2 =16.25 cm

for a convex lens, the image distance is equal to the object distance when object distance U = 2f where f is the focal length. Hence, in graph, OA = 2f and OB = 2f

average focal length of the lens, f = ( f1 + f2)/2 = ( 16.5 + 16.25 )/2 = 16.375 cm

average focal length of the lens, f = 16.375 cm

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