Question

The distance of real object when a concave mirror produces a real image of magnification ${}^{\prime }{m}^{\prime }$ is ($f$ is focal length)

• A. $\left(\frac{m-1}{m}\right)f$
• B. $\left(\frac{m+1}{m}\right)f$
• C. $(m-1)f$
• D. $(m+1)f$

Answer 1

The correct option is B $\left(\frac{m+1}{m}\right)f$

For concave mirror, using sign convention,

magnification, $m=\frac{-v}{u}$ (by definition)

Where, $u$ and $v$ are the distances of real object and real image.

Now, from the formula of concave mirror,

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

Or, $-\frac{1}{f}=\frac{1}{-u}+\frac{1}{-mu}$

$\therefore -\frac{1}{f}=-\left(\frac{m+1}{mu}\right)$

$\therefore u=\left(\frac{m+1}{m}\right)f$...........(B)