Correct Answer - Option 1 : 2 cm
The correct answer is 2 cm.
Explanation:
Given,
Height of the object = 6 cm
Focal length = f
Distance of the object (u)= - 4f [-ve in concave mirror]
radius (R) = 2f
The mirror formula is given by
\(\frac{1}{v}+\frac{1}{u}=-\frac{1}{f}\)
⇒\(\frac{1}{v}+\frac{1}{-4f}=-\frac{1}{f}\)
⇒\(\frac{1}{v}=\frac{1}{4f} -\frac{1}{f} = -\frac {3}{4f} \)
⇒\(v=-\frac{4f}{3}\)
Magnification \(m= -\frac {v}{u} = \frac {-4f/3}{4f} = - \frac {1}{3}\)
Now Height of the image ⇒ \(m =\frac {hi}{ho} = - \frac {1}{3}\)
⇒\(hi = - \frac {ho}{3} = - \frac {6}{3} = -2\) [Note: Image is inverted so its negative]
