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. Is there an error in this question or solution?
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. |