Which of the following expressions gives the linear magnification produced by a concave mirror of radius of curvature r, if U and V are the object and image distances respectively?
- \(\frac{V}{r}\) - 1
-
\(\frac{2V}{r}\) - 1
- \(\frac{U}{r}\) - 1
- \(\frac{2U}{r}\) - 1
The correct answer is: B
Explanation
F = \(\frac{r}{2}\) and v = mu
F = \(\frac{UV}{U + V}\)
\(\frac{r}{2}\) = \(\frac{U \times mu}{U + mu}\)
\(\frac{r}{2}\) = \(\frac{mu^2}{u(1 + m)}\)
\(\frac{r}{2} = \frac{mu}{1+m}\)
\(\frac{r}{2} = \frac{v}{1+m}\)
\(\frac{2v}{r} = 1+m\)
\(m = \frac{2v}{r} - 1\)