Question

Oliver has had a stamp collection since he was a boy. In BIO those days, holding a stamp 10 cm from his eye gave him a clear image. Now, his near point has receded to 90 cm, so he holds a magnifying lens directly in front of his eye to let him bring stamps closer. To the nearest diopter, what power lens enables him to focus on a stamp 10 cm away?

Answer 1

To focus on a stamp 10 cm away, Oliver will need a lens with a power of -9 diopters.

Step-by-step explanation:

To calculate the power of the lens required to focus on a stamp 10 cm away, we can use the lens formula:

1/f = 1/v - 1/u

Where f is the focal length of the lens, v is the image distance, and u is the object distance. In this case, the object distance is 10 cm and the image distance is the near point, which is 90 cm. Plugging in these values, we can solve for the focal length:

1/f = 1/90 - 1/10

1/f = 1/90 - 9/90 = -8/90

f = -90/8 ≈ -11.25 cm

The power of a lens is given by the equation:

P = 1/f

Converting the focal length to meters (since power is usually measured in diopters, which is 1/m), we get:

P ≈ 1/(-0.1125) ≈ -8.89 diopters

To the nearest diopter, the power lens that enables Oliver to focus on a stamp 10 cm away is -9 diopters.

Answer 2

To find the power of the lens for Oliver to focus on a stamp 10 cm away when his near point is at 90 cm, we use the lens formula, solve for the focal length in meters, and then find the lens power in diopters, rounding to the nearest whole number.

Step-by-step explanation:

To calculate the power of the lens Oliver needs to see a stamp at 10 cm clearly, we need to consider the lens formula which is given by 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the object distance, and di is the image distance. Here, the near point has receded to 90 cm; hence, we want an image to be formed at this distance when the stamp is 10 cm away from his eye. The lens power P is related to the focal length by P = 1/f (in meters), and the power is expressed in diopters (D).

Given di = 90 cm (0.9 m) and do = 10 cm (0.1 m), we plug these values into the lens formula getting 1/f = 1/0.1 - 1/0.9. Solving this gives us the focal length f. We then find the power P, ensuring to convert the focal length into meters before calculation.

The exact diopter value can be rounded to the nearest whole number as per the question's instructions. Remember, a positive lens power indicates a converging lens, which a farsighted person would use to see objects closer.