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# An object of length $2.5\;cm$ is placed at a $1.5\; f$ from a concave mirror where f is magnitude of focal length of mirror. The length of object is perpendicular to principal axis . Then which of following will be correct . (i) image is 5 cm long (ii) image is 10 cm long (iii) image is inverted (iv)image is erect

(a)both (i) and (iv)

(b)both (i) and (iii)

(c) both (ii) and (iii)

(d) both (ii) and (iv)

Focal length $F= -f$
and $u=-1.5\;f$
$\large\frac{1}{u}+\frac{1}{v}=\frac{1}{F}$
$\large\frac{1}{-1.5 \;f}+\frac{1}{v}=\frac{-1}{f}$
$\large\frac{1}{v}=\frac{1}{1.5 f}-\frac{1}{f}$
$\qquad= -\large\frac{-1}{3f}$
$v= -3 f$
Now $m =\large\frac{-v}{u}=\frac{-3 f}{1.5 \;f}$$=-2 or \large\frac{h_2}{h}$$=-2$
or $h_2=-2 h_1=-5 cm$
the image is 5 cm long.
The minus sign shows that it is inverted.
Hence c is the correct answer.

edited Jul 21, 2014