A convex lens and a concave lens, each having the same focal length of $25 ext{ cm}$, are put in contact to f

Question

A convex lens and a concave lens, each having the same focal length of $25	ext{ cm}$, are put in contact to form a combination of lenses. The power in dioptres of the combination is:

Accepted Answer

1.  **Focal Lengths with Sign Convention:** The focal length of a convex lens is positive, so $f_1 = +25	ext{ cm} = +0.25	ext{ m}$. The focal length of a concave lens is negative, so $f_2 = -25	ext{ cm} = -0.25	ext{ m}$.
2.  **Power of Individual Lenses:** The power $P$ of a lens in dioptres (D) is the reciprocal of its focal length in meters.
    *   Power of convex lens, $P_1 = \frac{1}{+0.25} = +4	ext{ D}$.
    *   Power of concave lens, $P_2 = \frac{1}{-0.25} = -4	ext{ D}$.
3.  **Power of Combination:** When two thin lenses are placed in contact, the equivalent power of the combination is the algebraic sum of their individual powers.
    *   $P_{eq} = P_1 + P_2 = +4	ext{ D} + (-4	ext{ D}) = 0	ext{ D}$.
4.  **Conclusion:** The power of the lens combination is zero.

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