What is the focal length of a convex lens of focal length 30 cm 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.

Solution

Given,
Focal length of the convex lens, f₁ = 30 cm
Focal length of concave lens, f₂ = –20 cm

Therefore, the focal length of the combination of lenses,

\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}

∴

\frac{1}{f} = \frac{1}{30} - \frac{1}{20} = \frac{2 - 3}{60} = \frac{- 1}{60}

f = - 60 cm

∴ The combination of lenses behaves as a concave lens as their focal length is negative. Hence, the system is not converging.

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Wave Optics

What is the focal length of a convex lens of focal length 30 cm 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.

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