The magnification by a lens is -3. Name the lens and state how are u and v related?

The magnification (m) of the lens is given as -3, which implies that the image is real and inverted because m is negative for a real and inverted image.

The image is enlarged as the magnitude of magnification is greater than 1.

As the image formed is real, inverted and magnified so the lens used is convex in nature.

As we know, the relation between u and v is as shown below —

$m = \dfrac{v}{u} \\[0.5em]$

Given,

m = -3

Substituting the values in the formula

$-3 = \dfrac{v}{u} \\[0.5em] \Rightarrow v = -3u \\[0.5em]$

Hence, the lens is convex in nature and the image distance v = -3u.