A person cannot see clearly objects more than 70.0 cm away. What power of corrective lens should be prescribed if the glass is to be worn 1.00 cm in front of the eye?
A) $1.45$ diopters
B) $- 1.45$ diopters
C) $- 0.0145$ diopters
D) $0.0145$ diopters

Question

A person cannot see clearly objects more than 70.0 cm away. What power of corrective lens should be prescribed if the glass is to be worn 1.00 cm in front of the eye? 
A) $1.45$ diopters
B) $- 1.45$ diopters
C) $- 0.0145$ diopters
D) $0.0145$ diopters

Quizplus · Accepted Answer

The person has a far point of 70.0 cm, meaning they can't see objects clearly beyond this distance. To correct this, the lens should form an image of a distant object at this far point. The lens formula is $1/f = 1/v - 1/u$, where $f$ is the focal length, $v$ is the image distance (70.0 cm from the eye, but since the lens is 1.00 cm in front of the eye, $v = 69.0 cm$), and $u$ is the object distance (considered infinite for distant objects). Since we're dealing with centimeters, we convert $v$ to meters: $v = 0.69 m$. Assuming $u$ is infinite, $1/f ≈ 1/v$, so $f ≈ v = 0.69 m$. The power $P$ of a lens is given by $P = 1/f$ (in meters), so $P ≈ 1/0.69 ≈ 1.45$ diopters. Because the lens must be converging to bring distant images into focus at the far point, and since converging lenses have positive focal lengths, but in this case, to correct for the person's inability to see distant objects (indicative of myopia or nearsightedness), a diverging lens is needed, which has a negative focal length, the correct answer is $-1.45$ diopters.

A Person Cannot See Clearly Objects More Than 70 1.451.451.45 Diopters B)

A Person Cannot See Clearly Objects More Than 70 $1.45$ Diopters
B)