Question

two thin lenses are in contact and the focal length of the combination is 80 cm. if the focal length of one lens is 20 cm, the focal length of the other would be.

Answer 1

To find the focal length of the second lens, we can use the lens maker's formula and solve for it using the given information and the focal length of the combination.

Step-by-step explanation:

To find the focal length of the second lens, we need to use the lens maker’s formula:

1/f = (n - 1)(1/R1 - 1/R2)

Assuming the lenses are thin, the radius of curvature can be approximated to infinity for both lenses. Therefore, the term 1/R1 - 1/R2 can be considered negligible.

Using the formula above, with the focal length of the combination (80 cm) and the focal length of one lens (20 cm), we can solve for the focal length of the other lens:

1/80 = (n - 1)(1/20)

1/80 = (n - 1)/20

(n - 1)/20 = 1/80

n - 1 = 20/80

n - 1 = 1/4

n = 1/4 + 1

n = 5/4

The refractive index, n, is approximately 5/4. Therefore, the focal length of the other lens would be:

1/f = (5/4 - 1)/20

1/f = 1/4*20

1/f = 1/80

f = 80 cm