A concave lens has a focal length of 30 cm. At what distance should the object from the lens be placed so that it forms an image at 20 cm from the lens?
60 cm in front of the lens
A concave lens always forms a virtual image on the same side as the object. Using the sign convention: f = −30 cm and v = −20 cm.
Lens formula: \( \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \).
\( \frac{1}{u} = \frac{1}{v} - \frac{1}{f} = -\frac{1}{20} + \frac{1}{30} = \frac{-3 + 2}{60} = -\frac{1}{60} \)
u = −60 cm; the negative sign means the object is on the same side as the incoming light, i.e. in front of the lens.
Hence, the answer is 60 cm in front of the lens.
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