A combination of thin lenses in contact
(A) helps to obtain diverging or converging lenses of desired magnification.
(B) has the net power equal to the algebraic sum of their individual powers.
(C) is used in designing lenses for many optical instruments.
(D) enhances sharpness of the image.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B), (C) and (D)
For thin lenses in contact the net power is \( P = P_{1} + P_{2} + P_{3} + \dots \), and the net magnification is the product of the individual magnifications.
(A) helps to obtain diverging or converging lenses of desired magnification. — Correct. By combining converging and diverging lenses of suitable powers, a system of the required power, and hence the required magnification, can be obtained.
(B) has the net power equal to the algebraic sum of their individual powers. — Correct. From \( 1/f = 1/f_{1} + 1/f_{2} + \dots \), \( P = P_{1} + P_{2} + \dots \), with converging lenses taken positive and diverging lenses negative.
(C) is used in designing lenses for many optical instruments. — Correct. The lenses of cameras, microscopes and telescopes are combinations of lenses.
(D) enhances sharpness of the image. — Correct. A suitable combination reduces the defects (aberrations) of a single lens, so the image is sharper.
NCERT (2026-27):
Combination of Thin Lenses in Contact – “… The derivation is valid for any number of thin lenses in contact. If several thin lenses of focal length \( f_1, f_2, f_3,\ldots \) are in contact, the effective focal length of their combination is given by
\( \displaystyle \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} + \frac{1}{f_3} + \ldots \qquad (9.31) \)
In terms of power, Eq. (9.31) can be written as
\( P = P_1 + P_2 + P_3 + \ldots \qquad (9.32) \)
where \( P \) is the net power of the lens combination. Note that the sum in Eq. (9.32) is an algebraic sum of individual powers, so some of the terms on the right side may be positive (for convex lenses) and some negative (for concave lenses). Combination of lenses helps to obtain diverging or converging lenses of desired magnification. It also enhances sharpness of the image. Since the image formed by the first lens becomes the object for the second, Eq. (9.25) implies that the total magnification \( m \) of the combination is a product of magnification \( (m_1, m_2, m_3,\ldots) \) of individual lenses
\( m = m_1 m_2 m_3 \ldots \qquad (9.33) \)
Such a system of combination of lenses is commonly used in designing lenses for cameras, microscopes, telescopes and other optical instruments.”
