If U is the object distance and V the image distance; which of the following expressions gives the linear magnification produced by a convex lens of focal length f?

A. ^u/_f + f
B. ^u/v +1
C. ^v/_f + 1
D. ^v/_f – 1

Correct Answer:

Option D = ^v/_f – 1

Explanation

Magnification, M = ^v/_u = v (¹/_u)
And for the Lens formula ¹/_u + ¹/_v = ¹/_f
=> ¹/_u = ¹/_f – ¹/_v
∴M = V(¹/_u)
= V(¹/_f – ¹/_v) = ^v/_f – ^v/_v = ^v/_f – 1
∴M = ^v/_f – 1