Question

Two thin lenses are of same focal length (f), but one is convex and the other is concave. When they are placed in opposite with each other, the equivalent focal of the combination will be:

• A. \(\frac{f}{4}\)
• B. \(\frac{f}{2}\)
• C. Infinite
• D. Zero

Answer 1

The Correct Option is C

The problem involves two thin lenses, one convex and one concave, each with the same focal length \( f \). To find the equivalent focal length \( F \) of the combination when placed in opposition, we use the formula for the equivalent focal length of two lenses in contact:

\(\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}\) 

Here, \( f_1 \) is the focal length of the convex lens, and \( f_2 \) is the focal length of the concave lens. Since they are of the same magnitude but opposite sign, we have:

\( f_1 = f \) and \( f_2 = -f \)

Substitute these values into the formula:

\(\frac{1}{F}=\frac{1}{f}+\frac{1}{-f}=\frac{1}{f}-\frac{1}{f}=0\)

If \(\frac{1}{F} = 0\), then the equivalent focal length \( F \) is infinite.

Therefore, the equivalent focal length of the lens combination is infinite.