How to Calculate the Focal Length of a Magnifying Glass Lens

How can we determine the focal length of a magnifying glass lens?

When a person with a near point at 13.2 inches uses a certain magnifying glass, it produces an angular magnification of 2.9 with the image very distant. What is the focal length of the lens of this magnifying glass?

Calculating the Focal Length of the Magnifying Glass Lens

The focal length of the lens of this magnifying glass is 20.15 inches.

To find the focal length of the lens of the magnifying glass, we can use the formula for angular magnification:

magnification = - (focal length / (near point - focal length))

We know that the person has a near point of 13.2 inches and the magnifying glass produces an angular magnification of 2.9. We also know that the image is very distant, which means that we can assume the image is at infinity. Therefore, we can simplify the formula to:

2.9 = - (focal length / (13.2 - focal length))

Solving for focal length, we get:

focal length = - (2.9 * (13.2 - focal length)) / 2.9

focal length = - (38.28 - 2.9 * focal length)

focal length = 2.9 * focal length - 38.28

1.9 * focal length = 38.28

focal length = 20.15 inches

Therefore, the focal length of the lens of this magnifying glass is 20.15 inches.