Final answer:
The power of the second lens when combined with a lens of focal length 20 cm to achieve an overall focal length of 80 cm is -3.75 diopters (D), which is option C.
Step-by-step explanation:
The student is asking about the focal length and power of a combination of two lenses that are in contact with each other. When two thin lenses are in contact, the formula for the combined focal length ℓ of the lenses is given by the reciprocal of the combined focal length equaling the sum of the reciprocals of the individual lenses' focal lengths:
1/ℓ = 1/f1 + 1/f2
We know the combined focal length is 80 cm, and one of the lenses has a focal length of 20 cm. To find the focal length of the second lens (f2), we rearrange the formula to solve for 1/f2:
1/f2 = 1/ℓ - 1/f1
1/f2 = 1/80 - 1/20
1/f2 = 1/80 - 4/80
1/f2 = -3/80
So, f2 = -80/3 cm. To find the power P (in diopters), we use the formula P = 1/f (with focal length in meters), so:
P = 1/(-80/3 × 0.01)
P = -3.75 D
Therefore, the power of the second lens is -3.75 D which corresponds to option C.