When an object is placed 20 cm in front of a concave mirror, a real image is formed. The image is three times magnified compared to the object. The focal length of the concave mirror can be calculated using the mirror equation:
frac1f=frac1v+frac1u
where:
Since the image is real and magnified, we have:
(m_{\text{linear}} = -\frac{v}{u} = 3)
Using the mirror equation, we can find the focal length:
(\frac{1}{f} = \frac{1}{v} + \frac{1}{u})
Substitute (v = 3u):
(\frac{1}{f} = \frac{1}{3u} + \frac{1}{u})
Solving for (f):
(f = \frac{u}{2})
Given that the object distance (u) is 20 cm, we find:
(f = \frac{20}{2} = 10 , \text{cm})
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