Two thin lenses with focal lengths s and r and separated by a distance d have their combined focal length given by the reciprocal of . Combine the fractions in the expression above and use the reciprocal of your result to find the combined focal length.

Question

Quizplus · Accepted Answer

Using the given formula:

1/f = 1/s + 1/r - d/sr

Taking the reciprocal:

f = 1 / (1/s + 1/r - d/sr)

Combining the fractions:

f = sr / (sr/s + sr/r - d)

f = sr / ((r+s)/(rs) - d)

f = sr / ((r+s-drs)/rs)

f = (1/rs) / ((r+s-drs)/s)

f = s / (s-r+d)

Therefore, the combined focal length is s / (s-r+d).

Substituting this formula into the given values, we get:

f = s / (s-r+d) = (30 cm) / (30 cm - 20 cm + 40 cm) = 30 cm / 50 cm = 0.6 cm

Therefore, the answer is B) 11ea984b_b2f3_26a2_9029_1b611f6a996f_TB4005_11.

Two Thin Lenses with Focal Lengths S and R and Separated