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NEET PHYSICSMedium

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

A

5

B

9

C

1

D

0.01

Step-by-Step Solution

Identify Given Data:

Focal length of first convex lens, $f_1 = +40 \text{ cm}$ .
Focal length of the sandwiched concave lens, $f_2 = -25 \text{ cm}$ .
Focal length of second convex lens, $f_3 = +40 \text{ cm}$ .

Calculate Power of Individual Lenses: The power $P$ of a lens in diopters (D) is given by $P = \frac{100}{f(\text{in cm})}$ .

Power of first convex lens: $P_1 = \frac{100}{40} = +2.5 \text{ D}$
Power of concave lens: $P_2 = \frac{100}{-25} = -4.0 \text{ D}$
Power of second convex lens: $P_3 = \frac{100}{40} = +2.5 \text{ D}$

Calculate Power of Combination: For thin lenses placed in contact, the equivalent power is the algebraic sum of their individual powers ( $P_{eq} = P_1 + P_2 + P_3$ ).

$P_{eq} = +2.5 \text{ D} - 4.0 \text{ D} + 2.5 \text{ D}$
$P_{eq} = +5.0 \text{ D} - 4.0 \text{ D} = +1 \text{ D}$

Conclusion: The total power of the combined lens system is $1 \text{ D}$ .

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