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Which of the following expressions gives the linear magni...

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

View answer & explanation

Correct answer is B

F = $\frac{r}{2}$ and v = mu

F = $\frac{UV}{U + V}$

$\frac{r}{2}$ = $\frac{U \times mu}{U + mu}$

$\frac{r}{2}$ = $\frac{mu^2}{u(1 + m)}$

$\frac{r}{2} = \frac{mu}{1+m}$

$\frac{r}{2} = \frac{v}{1+m}$

$\frac{2v}{r} = 1+m$

$m = \frac{2v}{r} - 1$

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