Thin lenses: A convex lens has a focal length f. An object is placed between infinity and 2f from the lens along a line perpendicular to the center of the lens. The image is located at what distance from the lens?

Question

Quizplus · Accepted Answer

According to the thin lens equation, 1/f = 1/d_o + 1/d_i, where f is the focal length, d_o is the object distance, and d_i is the image distance. If the object is between infinity and 2f, then d_o is positive and greater than infinity. Plugging these values into the thin lens equation and solving for d_i, we get:

1/f = 1/d_o + 1/d_i
1/f - 1/d_o = 1/d_i
d_i = f*d_o / (d_o - f)

Since d_o > f, the denominator (d_o - f) is positive, which means d_i is also positive. Therefore, the image is located on the same side of the lens as the object, and the distance from the lens is less than d_o (i.e. between the lens and the object). If we plug in d_o = 2f, we get:

d_i = f*d_o / (d_o - f) = f*(2f) / (2f - f) = 2f

So the image is located 2f away from the lens. The correct choice is C: between f and 2f.

Thin Lenses: a Convex Lens Has a Focal Length F