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: Option 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)