Question

"The reciprocal of focal length $f$ is equal to the sum of reciprocals of the object distance $u$ and the image distance $v$".

Make $v$ the subject of formula, obtained above

• A. $v=\frac{u}{u+f}$
• B. $v=\frac{f+u}{f}$
• C. $v=\frac{fu}{u-f}$
• D. $v=\frac{fu}{u+f}$

Answer 1

The correct option is C $v=\frac{fu}{u-f}$

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\frac{1}{f}=\frac{v+u}{uv}fv+uf=uvv(f-u)=-ufv=\frac{uf}{(u-f)}$