Question:easy

A convex and a concave lens are placed in contact. The focal lengths \( (F) \) of both are the same. The combination will behave:

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Powers add for lenses in contact; equal-magnitude convex \((+1/F)\) and concave \((-1/F)\) give zero net power, i.e. infinite focal length.
Updated On: Jul 10, 2026
  • as a concave lens.
  • as a convex lens.
  • as a planoconvex lens.
  • as a plane plate.
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The Correct Option is D

Solution and Explanation

Step 1: Use the combined-power rule.
Two thin lenses in contact form an equivalent lens whose power is the algebraic sum of the individual powers, \(P = P_1 + P_2\), with power \(P = 1/f\) measured in dioptres.

Step 2: Write the two powers with a common magnitude.
Both lenses have equal focal-length magnitude \(F\). Convex gives \(P_1 = +1/F\); concave gives \(P_2 = -1/F\). They are equal in size but opposite in sign.

Step 3: Cancel.
Adding, \(P = 1/F - 1/F = 0\). The converging action of the convex lens is exactly undone by the diverging action of the concave lens.

Step 4: Physical meaning.
Zero power corresponds to infinite focal length: rays pass through without net bending, just as through a flat sheet of glass. The combination therefore acts as a plane plate, option (iv).

\[\boxed{F_{comb} = \infty,\ \text{acts as plane plate}}\]
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