An object is placed 30 cm in front of a concave mirror of focal length 20cm. Calculate the distance between the object and the image.
Given:Object distance, \( u = 30 \,\text{cm} \)
Focal length of concave mirror, \( f = 20 \,\text{cm} \)
Using the mirror sign convention for a concave mirror:
\(u = -30 \,\text{cm}, \quad f = -20 \,\text{cm}\)
Using: \(\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\)
Substitute values:
\(\frac{1}{-20} = \frac{1}{-30} + \frac{1}{v}\)
\(\frac{1}{v} = -\frac{1}{20} + \frac{1}{30}\)
=\(\frac{-3 + 2}{60}\)
= -\(\frac{1}{60}\)
\(v = -60 \,\text{cm}\)
Distance between object and image:
\(= |v - u| = |-60 - (-30)| = 30 \,\text{cm}\)
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