Q.Two thin lenses of power +4D and -2D are placed in contact with each other. What is the focal length of the lens combination?
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🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Power of a Lens and Combination of Lenses
The power of a lens is a measure of how strongly it converges or diverges light, defined as P=1/f (SI unit dioptre, D; 1D=1m−1), positive for a converging lens and negative for a diverging one; from the lens maker's formula, P=(n−1)(R11−R21), so a higher refractive index or more sharply curved (smaller-radius, 'bulkier') surfaces give greater power (and hence a shorter focal length), while gently curved ('skinny') lenses have low power. For two thin lenses of focal lengths f1,f2 placed in contact (a common optical centre), writing and adding the lens equation for each in turn (the first lens's image serving as the second lens's object) gives the effective focal length F1=f11+f21, extendable to any number of lenses as F1=∑fi1, or equivalently as an algebraic sum of powers P=P1+P2+… (some positive for convex, some negative for concave); the total magnification of the combination is the product of the individual magnifications, m=m1×m2×⋯. Two thin lenses can even combine to give zero net power (P1=−P2) if a converging and a diverging lens of exactly matching magnitudes are used together. When two thin lenses of focal length f1,f2 are separated by a distance d and only paralle …
Powers of thin lenses placed in contact add up algebraically, so combining the converging and the diverging power leaves a net power whose reciprocal is the focal length of the combination. …
Powers of thin lenses in contact simply add; adding +4D and −2D gives +2D, whose reciprocal is the combined focal length.
For two thin lenses in contact, the net power is the algebraic sum of the individual powers:
P = P1 + P2 = (+4 D) + (−2 D) = +2 D
Focal length f = 1/P (with P in dioptres, f in metres):
f = 1/2 m = 0.5 m = 50 cm
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Showing the 12 most recent of 32 on this concept.
- CBSE 2026Set ANNUAL1 markMCQQ.If power of a lens is +2 dioptre, then it is -(i) Concave lens of focal length 50 cm.(ii) Convex lens of focal length 500 mm(iii) Concave lens of focal length 0.25 m.(iv) Convex lens of focal length 25 cm.
›Reveal solutionSolution
f = 1/P; positive power means a convex (converging) lens.
Power P=+2 D, so f=P1=21 m=0.5 m=50 cm=500 mm. Since the power is positive, the …
- CBSE 2026Set ANNUAL1 markMCQQ.Focal length of field lens of power 2D is:(a) 50 cm(b) –50 cm(c) 200 cm(d) –200 cm
›Reveal solutionSolution
Focal length is the reciprocal of power; for P=2D, f=0.5m=50cm.
Power of a lens is P=f(in metres)1. Given P=2D: f=P1=21=0.5m=50cm. Since the power is …
- CBSE 2025Set D1 markMCQQ.If two converging lenses of equal focal length f are kept in contact then the focal length of the combination will be (A) f (B) 2f (C) f/2 (D) 3f
›Reveal solutionSolution
For thin lenses in contact powers add: P = P₁ + P₂, giving F = f/2 for two equal lenses.
When two thin lenses are placed in contact, their combined power is the sum of the individual powers:
1/F = 1/f₁ + 1/f₂
With f₁ = f₂ = f:
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- CBSE 2025Set D1 markMCQQ.Power of a convex lens is 2 dioptre. Its focal length will be (A) 20 cm (B) 50 cm (C) 40 cm (D) 60 cm
›Reveal solutionSolution
Focal length (in metres) is the reciprocal of power in dioptres: f = 1/P.
The power of a lens is P = 1/f, with f in metres. For P = 2 D:
f = 1/P = 1/2 = 0.5 m = 50 cm
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- CBSE 2025Set A1 markQ.Write answer in one sentence: What is power of a lens having +0.5 m focal length?
›Reveal solutionSolution
A lens with focal length +0.5 m has power +2 dioptre.
The power of a lens is defined as the reciprocal of its focal length expressed in metres:
P=f(in metres)1
Here f=+0.5 m (positive, by sign convention for a converging/convex lens):
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- CBSE 2025Set ANNUAL1 markMCQQ.Two thin lenses of focal length f1 and f2 are placed in contact with each other, the effective focal length of the combination will be(a) f = f1 + f2(b) f = f1 - f2(c) f = (f1 + f2) / (f1 f2)(d) f = (f1 f2) / (f1 + f2)
›Reveal solutionSolution
For thin lenses in contact, the powers (reciprocals of focal length) simply add, so the combined focal length is the product over the sum of the individual focal lengths.
For a single thin lens, the lens maker's relation for an object gives v1−u1=f1. For two thin lenses of focal length f1,f2 placed in contact, the image formed by the first lens acts as the object for the second. Adding the two lens equations for the combination:
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- CBSE 2025Set ANNUAL1 markMCQQ.If the focal length of a lens is f metre, then the value of its power will be(a) f dioptre(b) 1/f dioptre(c) (1 - f) dioptre(d) 100/f dioptre
›Reveal solutionSolution
The power of a lens is defined as P = 1/f, with f measured in metres, giving power in dioptres (D).
By definition, lens power P (in dioptres) is the reciprocal of the focal length f (in metres):
P = 1/f
…
- CBSE 2025Set ANNUAL1 markQ.Two thin lenses of power + 4D and – 2D are in contact. The focal length of the combination is ______.
›Reveal solutionSolution
Powers of thin lenses in contact simply add; here P = (+4 D) + (−2 D) = +2 D, giving f = 1/P = 0.5 m.
For two thin lenses of powers P1 and P2 placed in contact (coaxially, touching), the power of the combination is the algebraic sum:
P=P1+P2
Here P1=+4 D and P2=−2 D, so:
P=4+(−2)=+2 D
Since power and focal length are related by P=f1 (f in metres): …
- CBSE 2025Set ANNUAL1 markMCQQ.The tangent of the angle by which it converges or diverges a beam of light parallel to the principle axis falling at unit distance from optical centre is called:(a) Malus law(b) Lens formula(c) Power of a lens(d) Snell's law.
›Reveal solutionSolution
The power of a lens is defined exactly as the tangent of the angle of convergence/divergence produced in a ray at unit distance from the optical centre.
If a parallel beam of light, on refraction through a lens, converges or diverges through an angle θ at unit distance from the optical centre, the power of the lens is P=tanθ, which for small angles equals 1/f (f in metres), measured in dioptres (D). A convex (converging) lens has positive power, a conca …
- CBSE 2025Set ANNUAL1 markMCQQ.Two thin lenses of focal length f1 and f2 are in contact and coaxial. The power of the combination is –(a) (f1 + f2)/2(b) (f1 + f2)/(f1 f2)(c) sqrt(f1/f2)(d) sqrt(f2/f1)
›Reveal solutionSolution
For thin lenses in contact, powers simply add.
For two thin lenses of focal lengths f1 and f2 placed in contact and coaxially, the powers add algebraically:
…
- CBSE 2024Set IMPROVEMENT1 markQ.Power of a convex lens is +2 D. Find its focal length.
›Reveal solutionSolution
Focal length is the reciprocal of power: f=1/P.
The power of a lens is related to its focal length (in metres) by P=f1. Given P=+2 D:
f=P1=21=0.5 m=50 cm …
- CBSE 2024Set A1 markMCQQ.Powers of two lenses kept in contact, are P₁ and P₂. The power of equivalent lens will be (A) P₁/P₂ (B) P₂/P₁ (C) P₁ × P₂ (D) P₁ + P₂
›Reveal solutionSolution
Powers of thin lenses in contact add up: P = P₁ + P₂.
For two thin lenses of focal lengths f1 and f2 placed in contact, the equivalent focal length is
f1=f11+f21.
Since power is the reciprocal of focal length, P=1/f (with f in metres), this becomes
P=P1+P2.
…
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