A point object is placed at a distance of 15cm from a convex lens. The image is formed on the other side at a distance of 30cm from the lens. When a concave lens is placed in contact with the convex lens, the image shifts away further by 30cm. Calculate the focal lengths of the two lenses.
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Let u = object distance from convex lens = -15cm
$v_1 =$ image distance from convex lens when alone = 30cm
$f_1 =$ focal length of convex lens.
Now, $\therefore \ \frac{1}{\text{v}_1}+\frac{1}{\text{u}}=\frac{1}{\text{f}_1}$
or, $\frac{1}{\text{f}_1}=\frac{1}{30}-\frac{1}{-15}=\frac{1}{30}+\frac{1}{15}$
or, $\text{f}_1=10\text{cm}$
Again, Let v = image (final) distance from concave lens = +(30 + 30) = 60cm
$v_1 =$ object distance from concave lens = +30m
$f_2 =$ focal length of concave lens
Now, $\therefore \ \frac{1}{\text{v}}-\frac{1}{\text{v}_1}=\frac{1}{\text{f}_1}$
Or, $=\frac{1}{\text{f}_1}=\frac{1}{60}-\frac{1}{30}\Rightarrow\text{f}_2=-60\text{cm}.$
So, the focal length of convex lens is 10cm and that of concave lens is 60cm.
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