A lens of focal length 20 cm forms an inverted image at a distance 60 cm from the lens.
Calculate the magnification of the image.
Topic: Lenses and image formation
Answer
Given: focal length f = +20 cm, image distance v = +60 cm (real, inverted image)
First find u from the lens formula: 1/v − 1/u = 1/f 1/60 − 1/u = 1/20 −1/u = 1/20 − 1/60 −1/u = 3/60 − 1/60 = 2/60 = 1/30 u = −30 cm
Magnification, m = v ÷ u = (+60) ÷ (−30) = −2
Magnification = −2
The image is twice the size of the object and inverted.
The question gives f and v, so u has to be found first — do not try to read it off the question, it is not there.
Rearranging for 1/u is where signs go astray. Move the 1/u term across carefully: 1/60 − 1/u = 1/20 becomes −1/u = 1/20 − 1/60, and the minus sign on the left is what makes u negative, as it must be for a real object.
Read the final answer in words: the minus means inverted, the 2 means double size. That matches an object placed between F and 2F for a convex lens, which is where 30 cm sits (between 20 and 40).