Read the following passage and answer the questions.
Aman sets up a thin convex glass lens of focal length 20 cm on an optical bench. He places a lighted candle on one side of the lens and a white screen on the other side. He moves the candle to several positions. Each time, he slides the screen until a sharp image of the flame appears on it. For some positions of the candle, no image can be caught on the screen at all. He then removes the screen and looks at the candle through the lens. In one trial, he places the lens in a glass tank filled with water. In another trial, he places a thin concave lens in contact with the convex lens and looks for the new image. His teacher asks him to note the image distance and the size of the image each time. She also asks him to write the power of each lens in dioptre.
Consider the following statements about Aman’s experiment:
(A) The power of the convex lens used by Aman is +5 D.
(B) With the concave lens in contact, the power of the combination is the algebraic sum of the powers of the two lenses.
(C) The magnification produced by the two lenses in contact is the sum of their separate magnifications.
(D) The thin lens formula holds for a convex lens but not for a concave lens.
Which of the above statements are correct? Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) and (B) only
Power is the reciprocal of the focal length in metre. For thin lenses in contact, powers add, while magnifications multiply.
(A) The power of the convex lens used by Aman is +5 D. — True. The focal length is 20 cm, that is, 0.20 m.
\( \begin{aligned} P &= \frac{1}{f} \\ &= \frac{1}{0.20\ \mathrm{m}} \\ &= +5\ \mathrm{D} \end{aligned} \)
(B) With the concave lens in contact, the power of the combination is the algebraic sum of the powers of the two lenses. — True. The net power is \( P=P_1+P_2 \). The concave lens has a negative power, so the sum is an algebraic sum.
(C) The magnification produced by the two lenses in contact is the sum of their separate magnifications. — False. For lenses in contact the magnifications multiply, \( m=m_1m_2 \). They are not added.
(D) The thin lens formula holds for a convex lens but not for a concave lens. — False. The same formula works for a concave lens; only its focal length is taken as negative.
NCERT (2026-27):
Power of a lens – “The SI unit for power of a lens is dioptre (D): 1D = 1m–1. The power of a lens of focal length of 1 metre is one dioptre. Power of a lens is positive for a converging lens and negative for a diverging lens. …”
Combination of thin lenses in contact – “… Note that the sum … is an algebraic sum of individual powers, so some of the terms … may be positive (for convex lenses) and some negative (for concave lenses). …”
Combination of thin lenses in contact – “… Since the image formed by the first lens becomes the object for the second, … the total magnification m of the combination is a product of magnification (m1, m2, m3,...) of individual lenses …”
Refraction by a lens – “… Though we derived it for a real image formed by a convex lens, the formula is valid for both convex as well as concave lenses and for both real and virtual images.”