A student places an object at 90 cm from a concave mirror and finds the image at 45 cm in front of the mirror. What will be the distance between the pole and the principal focus of this mirror?
30 cm
The distance between the pole and the principal focus is the focal length of the mirror.
Using the sign convention, object distance u = -90 cm and the image in front of the mirror gives v = -45 cm.
Mirror formula: \(\frac{1}{f} = \frac{1}{v} + \frac{1}{u} = -\frac{1}{45} - \frac{1}{90} = -\frac{3}{90} = -\frac{1}{30}\)
So f = -30 cm, i.e. the principal focus is 30 cm from the pole.
Hence, the answer is 30 cm.
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