A convex lens of focal length

Question

f, forms a real image whose size is the same as that of the object.
The object distance is equal
A. 4F
B. 2F
C. F
D. F/2
E. F/4

Answer 1

The correct answer is C. F.

The magnification of a convex lens is given by the formula:

magnification (m) = (-) image distance (i) / object distance (o)

In this case, since the size of the image is the same as that of the object, the magnification is equal to 1. Therefore:

1 = (-) i / o

Since the object distance is equal to the focal length of the lens (o = f), we can substitute this into the equation:

1 = (-) i / f

Rearranging the equation, we get:

i = (-) f

This means that the image distance is equal to the negative value of the focal length. In other words, the real image is formed on the opposite side of the lens compared to the object, and its distance is equal to the focal length.

Therefore, the object distance is equal to the focal length, or option C. F.