Question

A thin biconvex lens has radii of curvature of R1 = +50 cm and R2 = −50 cm and with index of refraction 1.7. If the lens is then set on a stand, where does sunlight come to a focus relative to the position of the lens?

Answer 1

The sunlight comes to a focus 71.43 cm from the lens.

Step-by-step explanation:

To find where sunlight comes to a focus relative to the position of the lens, we can use the lens equation:

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

where f is the focal length of the lens, n is the index of refraction, R1 is the radius of curvature of the first surface, and R2 is the radius of curvature of the second surface.

Substituting the given values:

R1 = 50 cm, R2 = -50 cm, n = 1.7

we can calculate the focal length:

1/f = (1.7 - 1) * (1/50 - 1/-50)

1/f = 0.7 * (1/50 + 1/50)

1/f = 0.7 * (2/50)

1/f = 0.014

f = 1/0.014

f = 71.43 cm

Since the lens is thin, the sunlight will come to a focus on the opposite side of the lens at a distance of 71.43 cm from the lens.