Question

as part of an experiment, justin determined that the focal length of a three-lens system was 4.0 cm. justin's partner, james, was supposed to record the individual focal lengths of the three lenses. unfortunately, in his hurry to get to lunch, james only recorded the values for two of the lenses: 40.0 cm and 12.5 cm. what was the focal length of the third lens?

Answer 1

The focal length of the third lens in a three-lens system, given the total focal length and the focal lengths of the other two lenses, can be determined using the formula for combining lenses in series. The third lens is found to have an approximate focal length of 6.15 cm.

Step-by-step explanation:

Justin determined that the focal length of a three-lens system was 4.0 cm. Two of the lenses have focal lengths of 40.0 cm and 12.5 cm respectively. To find the focal length of the third lens, we'll use the formula for combining lenses in series:

1/ftotal = 1/f1 + 1/f2 + 1/f3

Where ftotal is the total focal length of the system (4.0 cm), and f1, f2, f3 are the focal lengths of each lens.

Using the values given:

1/4.0 cm = 1/40.0 cm + 1/12.5 cm + 1/f3

Solving for 1/f3:

1/f3 = 1/4.0 cm - (1/40.0 cm + 1/12.5 cm)

This gives us the reciprocal of the focal length of the third lens. Taking the reciprocal of both sides will then give us the focal length of the third lens.

Calculating this value, we find that the focal length of the third lens is approximately 6.15 cm. Therefore, the third lens has a focal length of 6.15 cm.