What is the focal length of a convex lens of focal length 30cm in contact with a concave lens of focal length 20 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.
Exercise
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Focal length of the convex lens, $f_1 = 30$ cm
Focal length of the concave lens, $f_2 = - 20$ cm
Focal length of the system of lenses = f
The equivalent focal length of a system of two lenses in contact is given as:
$\frac{1}{\text{f}}=\frac{1}{\text{f}_1}+\frac{1}{\text{f}_2}$
$\frac{1}{\text{f}}=\frac{1}{30}-\frac{1}{20}=\frac{2-3}{60}=-\frac{1}{60}$
$\therefore \ \text{f}=-60 \ \text{cm}$
Hence, the focal length of the combination of lenses is 60 cm. The negative sign indicates that the system of lenses acts as a diverging lens.
Focal length of the concave lens, $f_2 = - 20$ cm
Focal length of the system of lenses = f
The equivalent focal length of a system of two lenses in contact is given as:
$\frac{1}{\text{f}}=\frac{1}{\text{f}_1}+\frac{1}{\text{f}_2}$
$\frac{1}{\text{f}}=\frac{1}{30}-\frac{1}{20}=\frac{2-3}{60}=-\frac{1}{60}$
$\therefore \ \text{f}=-60 \ \text{cm}$
Hence, the focal length of the combination of lenses is 60 cm. The negative sign indicates that the system of lenses acts as a diverging lens.
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