An object 2cm high is placed at a distance

Asked by admin @ 23/08/2021 in Physics viewed by 336 People

an object 2cm high is placed at a distance of 16cm from a concave mirror which produces a real image 3cm high. what is focal length of the mirror and position of the image??????

Answered by admin @ 23/08/2021

Height of the object, h1 = 2 cm
height of the image, h2 = -3 cm
object distance, u = -16cm
image distance = v

magnification = $\frac{h2}{h1} = \frac{-v}{u}$

⇒ $\frac{-3}{2} = \frac{-v}{-16}$

⇒ $(-16)*(-3)=2*(-v)$
⇒ $v = - \frac{48}{2} =-24cm$

From mirror formula
$\frac{1}{u} + \frac{1}{v} = \frac{1}{f} \\ \\ \frac{1}{-16} + \frac{1}{-24} = \frac{1}{f} \\ \\ \frac{3+2}{-48} = \frac{1}{f} \\ \\ \frac{5}{-48} = \frac{1}{f} \\ \\ f= \frac{-48}{5} = -9.6cm$

So focal length is 9.6cm and image distance is 24cm(to the left of mirror)

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