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?
A. \(\frac{V}{r}\) - 1 B. \(\frac{2V}{r}\) - 1 C. \(\frac{U}{r}\) - 1 D. \(\frac{2U}{r}\) - 1
Correct Answer: B
Explanation
F = \(\frac{r}{2}\) and v = mu F = \(\frac{UV}{U + V}\) \(\frac{r}{2}\) = \(\frac{U \times mu}{U + mu}\) \(\frac{r}{2}\) = \(\frac{mu^2}{u(1 + m)}\) \(\frac{r}{2} = \frac{mu}{1+m}\) \(\frac{r}{2} = \frac{v}{1+m}\) \(\frac{2v}{r} = 1+m\) \(m = \frac{2v}{r} - 1\)
