Question

An image is 4.0 mm in front of a converging lens with a focal length of magnitude 5.0 mm. Where is the object for this image?

A. 9.0 mm behind the lens
B. 2.2 mm in front of the lens
C. 20 mm in front of the lens
D. 2.2 mm behind the lens

Answer 1

Using the lens formula, 1/f = 1/do + 1/di, with the given values for a converging lens, the object distance comes out to be approximately 20 mm in front of the lens, making the correct answer C: 20 mm in front of the lens.

Step-by-step explanation:

To determine where the object is for a given image in front of a converging lens, we'll use the lens formula, which is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. Since we're given that the image is 4.0 mm in front of a converging lens (which means di is -4.0 mm, as the image is on the same side as the object) with a focal length of 5.0 mm, we can rearrange the lens formula to solve for do.

Plugging the values into the lens formula, we get: 1/5.0 mm = 1/do - 1/(-4.0 mm). Solving for do yields an object distance of approximately 20 mm in front of the lens. So, the answer is C: 20 mm in front of the lens.