Question

Sunlight is observed to focus at a point 15.9 cm behind a lens.

What kind of lens is it?
a. converging lens
b. diverging lens

What is its power in diopters? Follow the sign conventions.
Express your answer using three significant figures.
P=____

Answer 1

The lens is a converging lens and its power in diopters is approximately 6.29 D, calculated using the inverse of its focal length in meters.

Step-by-step explanation:

If sunlight is observed to focus at a point 15.9 cm behind a lens, the lens in question is a converging lens. This is because a converging lens (also known as a convex lens) gathers parallel light rays and concentrates them to a focal point on the opposite side of the lens. According to sign conventions, the focal length of a converging lens is positive if the focal point is on the opposite side of the lens relative to the incoming light.

The power (P) of a lens in diopters (D) is given by the inverse of its focal length in meters. Therefore, to calculate the power of the lens:

1. Convert the focal length from centimeters to meters: f = 15.9 cm = 0.159 m.
2. Calculate the power using the formula P = 1/f: P = 1/0.159 m ≈ 6.29 D.

So, the power of the lens is approximately 6.29 diopters.