An eye specialist prescribes spectacles having a combination of a converging lens of focal length 25 cm and a diverging lens of focal length of 20 cm. The power of the combination of two lenses (in dioptre) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -1.0
Given:
Focal length of converging lens = $f_1 = +25 \text{ cm} = +0.25 \text{ m}$
Focal length of diverging lens = $f_2 = -20 \text{ cm} = -0.20 \text{ m}$
Power of each lens:
$P_1 = \frac{1}{f_1} = \frac{1}{0.25} = +4 \text{ D}$
$P_2 = \frac{1}{f_2} = \frac{1}{-0.20} = -5 \text{ D}$
Total power of combination:
$P = P_1 + P_2 = 4 + (-5) = -1 \text{ D}$
The power of the combination is $-1 \text{ dioptre}$.