A student observes that when an object is placed at 15 cm from a mirror, the image is formed at 30 cm on the same side. What is the focal length of the mirror?
-10 cm
An image formed on the same side as the object (in front of the mirror) is real, so the mirror is concave.
Using the sign convention, u = -15 cm and v = -30 cm.
Mirror formula: \(\frac{1}{f} = \frac{1}{v} + \frac{1}{u} = -\frac{1}{30} - \frac{1}{15} = -\frac{3}{30} = -\frac{1}{10}\)
So f = -10 cm.
Hence, the answer is -10 cm.
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