Final answer:
The power of the lens that turns a candle's light into a parallel beam is found by taking the reciprocal of the focal length in meters. Since the lens focuses parallel light at an object distance of 40 cm, the focal length is 0.40 m and the power is 2.5 D.
Step-by-step explanation:
Finding the Power of a Lens
The question asks about the power of the lens that can convert a parallel beam from a candle placed 40 cm away. In optics, the power of a lens is inversely proportional to its focal length. It's defined as the reciprocal of the focal length (in meters) and is measured in diopters (D). To find the power of a lens, the equation P = 1/f is used, where P is the power in diopters and f is the focal length in meters.
Since the candle's light comes out as a parallel beam after passing through the lens, we can deduce that the lens is focusing the light at infinity, which suggests that the focal length of the lens is equal to the distance of the candle from the lens. Given that the distance is 40 cm, to find the power in diopters, we must first convert this distance to meters by dividing by 100; thus, 40 cm is 0.40 meters. Then the power P is calculated as follows:
P = 1/f = 1/0.40 = 2.5 D
Therefore, the power of the lens is 2.5 diopters.