Question

An object is placed at a distance 2f from the pole of a convex mirror of focal length f​​​​​​. Then, the magnification is?

Answer 1

Step 1: Given

Focal length(f)=f

Object distance(u)=-2f

v and m is image distance and magnification respectively.

Step 2: Formula used

$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$ (mirror formula)

$m=-\frac{v}{u}$

Step 3: Finding image distance

$\frac{1}{-2f}+\frac{1}{v}=\frac{1}{f}$

$\frac{1}{v}=\frac{1}{f}+\frac{1}{2f}$

v=$\frac{2f}{3}$

Now, magnification(m) = -v(image distance)/u(object distance)

m=$\frac{\frac{-2f}{3}}{-2f}$ = $+\frac{1}{3}$

Hence, the magnification is $+\frac{1}{3}$ .