A concave lens with a focal length of $-25 ext{ cm}$ is sandwiched between two convex lenses, each with a fo

Question

A concave lens with a focal length of $-25 	ext{ cm}$ is sandwiched between two convex lenses, each with a focal length of $40 	ext{ cm}$. The power (in diopters) of the combined lens system would be:

Accepted Answer

1. **Identify Given Data:** 
   - Focal length of first convex lens, $f_1 = +40 	ext{ cm}$.
   - Focal length of the sandwiched concave lens, $f_2 = -25 	ext{ cm}$.
   - Focal length of second convex lens, $f_3 = +40 	ext{ cm}$.
2. **Calculate Power of Individual Lenses:** The power $P$ of a lens in diopters (D) is given by $P = \frac{100}{f(	ext{in cm})}$.
   - Power of first convex lens: $P_1 = \frac{100}{40} = +2.5 	ext{ D}$
   - Power of concave lens: $P_2 = \frac{100}{-25} = -4.0 	ext{ D}$
   - Power of second convex lens: $P_3 = \frac{100}{40} = +2.5 	ext{ D}$
3. **Calculate Power of Combination:** For thin lenses placed in contact, the equivalent power is the algebraic sum of their individual powers ($P_{eq} = P_1 + P_2 + P_3$).
   - $P_{eq} = +2.5 	ext{ D} - 4.0 	ext{ D} + 2.5 	ext{ D}$
   - $P_{eq} = +5.0 	ext{ D} - 4.0 	ext{ D} = +1 	ext{ D}$
4. **Conclusion:** The total power of the combined lens system is $1 	ext{ D}$.

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