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.
Focal length of the convex lens, f1 = 30 cm
Focal length of the concave lens, f2 = −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:
`1/"f" = 1/"f"_1 + 1/"f"_2`
`1/"f" = 1/30 - 1/20`
= `(2 - 3)/60`
= `-1/60`
∴ f = −60 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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What is the focal length of a convex lens of focal length 30cm in contact with a concave lens of focal length 20cm? Is the system a converging or a diverging lens? Ignore the thickness of the lenses.
Answer:
According to the question –
Focal length of the convex lens is f1=30cm
Focal length of the concave lens is f2= -20cm
Focal length of the system of lenses is denoted by f
The equivalent focal length of the given system of lenses is given as:
$\frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$
$\frac{1}{f}=\frac{1}{30}-\frac{1}{20}=\frac{2-3}{60}=-\frac{1}{60}$
Therefore f=-60cm
As a result, the focal length of the lens combination is 60cm. In addition, the negative sign indicates that the lens system in use is a diverging lens.