Q.Focal length of each lens shown in the figure below is 10 cm. Find the distance of the final image of point object O from the convex lens. Draw the ray diagram also. [FIGURE: A point object O lies on the principal axis, 20 cm to the left of a convex (double-convex) lens of focal length 10 cm. A second lens — biconcave (diverging), focal length 10 cm — is placed 30 cm to the right of the convex lens, on the same principal axis.]

Showing the 12 most recent of 18 on this concept.

1. CBSE 2026Set ANNUAL1 markMCQ
   Q.The diagram depicts a

   (a) concave lens

   (b) convex lens

   (c) plane sheet of glass since it is of equal thickness

   (d) convexo-concave lens

   ›Reveal solutionSolution

   The sketched cross-section — thin at the centre, thicker towards the edges — is the standard simplified symbol for a diverging (concave) lens, as opposed to a convex lens (thick at the centre) or a plane sheet of glass (uniform thickness with flat, parallel faces).

   Reasoning from the shape of the diagram

   Lenses are conventionally distinguished in simplified textbook cross-section diagrams by how their thickness varies from the optical centre to the edge:

   • A convex (converging) lens bulges outward: it is thickest at the centre and thinner at the edges.
   • A concave (diverging) lens curves inward at both faces: it is thinnest at the centre and thicker at the edges (a crescent-like shape when only the outline is sketched).
   • A plane sheet of glass has two flat, parallel faces and therefore uniform thickness everywhere. …

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2. CBSE 2024Set IMPROVEMENT1 markMCQ
   Q.Two convex lenses of same focal length $f$ are in mutual contact. If focal length of this lens combination is $F$ then —

   (a) $F<f$

   (b) $F>f$

   (c) $F=\infty$

   (d) $F=f$

   ›Reveal solutionSolution

   Two lenses of focal length $f$ each, in contact, combine to give $F=f/2$, which is less than $f$.

   …

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3. CBSE 2024Set ANNUAL1 mark
   Q.For a convex lens, in which position an object should be placed so as to have real and magnified image?

   ›Reveal solutionSolution

   A convex lens forms a real, magnified image only when the object lies between F and 2F.

   For a thin convex (converging) lens, the nature, size and position of the image depend on where the object is placed relative to the focal point F and the point 2F:

   • Object beyond 2F → real, inverted, DIMINISHED image between F and 2F on the other side.
   • Object exactly at 2F → real, inverted image of the SAME size, also at 2F.
   • Object between F and 2F → real, inverted, MAGNIFIED image formed beyond 2F on the other side.
   • Object at F → image at infinity (highly magnified, not usable as a real finite image).
   • Object between the lens and F → virtual, erect, magnified image on the same side (used as a simple magnifier). …

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4. CBSE 2023Set ANNUAL1 markMCQ
   Q.The focal length of concave lens is 20 cm. Its power is :

   (a) - 0.2 D

   (b) + 5 D

   (c) - 5 D

   (d) infinity

   ›Reveal solutionSolution

   A concave lens of focal length 20 cm has power -5 D.

   Power P = 1/f, with f in metres. For a concave (diverging) lens the focal length is negative: f = -20 cm = -0.20 m.

   P = 1/(-0.20) = -5 D. …

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5. CBSE 2022Set ANNUAL1 mark
   Q.Two thin lenses of power +5 Dioptre and -3 Dioptre are placed in contact. Find the power of this combination.

   ›Reveal solutionSolution

   For thin lenses in contact the powers add: $P = 5 + (-3) = +2$ D.

   When two thin lenses are placed in contact, the equivalent power is the algebraic sum of the individual powers:

   $P = P_1 + P_2.$

   Here $P_1 = +5$ D (convex) and $P_2 = -3$ D (concave):

   $P = (+5) + (-3) = +2 \text{ D}.$

   …

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6. CBSE 2020Set XS1 mark
   Q.Define second focus of a concave lens.

   ›Reveal solutionSolution

   It is the virtual point from which parallel incident rays seem to diverge after passing through the diverging lens.

   Definition. The second principal focus $F_2$ of a lens is the point associated with rays that strike the lens parallel to the principal axis.

   For a concave (diverging) lens, such parallel rays diverge after refraction. When produced backwards they appear to meet at a point on the principal axis on the same side as the incident light. That point is the second focus $F_2$; it is a virtual focus, and the focal length is take …

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7. CBSE 2019Set ANNUAL1 mark
   Q.For which position of the object magnification of convex lens is –1. (minus one)?

   ›Reveal solutionSolution

   $m = -1$ for a convex lens occurs when the object is at a distance $2f$ from the lens; the image is then real, inverted and equal in size.

   Concept. Linear magnification of a lens is $m = \dfrac{v}{u}$. A value $m = -1$ means the image is the same size as the object but inverted (real image).

   …

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8. CBSE 2019Set ANNUAL1 mark
   Q.Write the SI unit for power of a lens.

   ›Reveal solutionSolution

   SI unit of lens power = dioptre (D) = $\text{m}^{-1}$.

   Concept. The power of a lens measures its ability to converge or diverge light and is defined as the reciprocal of its focal length expressed in metres:

   $P = \frac{1}{f\,(\text{in metres})}$

   …

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9. CBSE 2019Set ANNUAL1 markMCQ
   Q.Cylindrical lenses are used to correct the eye defect called -

   (a) myopia

   (b) hypermetropia

   (c) astigmatism

   (d) presbyopia

   ›Reveal solutionSolution

   Cylindrical lenses correct astigmatism.

   In astigmatism the cornea (or lens) is not equally curved in all planes, so it focuses horizontal and vertical lines differently and the eye cannot see both sharply at once. A cylindrical lens has power in only one plane, so it can compensate for the unequal curvature. …

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10. CBSE 2019Set ANNUAL1 markMCQ
    Q.Equivalent focal length of two lenses in contact having power - 15 D and + 5 D will be -

    (a) - 20 cm

    (b) - 10 cm

    (c) + 10 cm

    (d) + 20 cm

    ›Reveal solutionSolution

    P = P₁ + P₂ = −15 + 5 = −10 D ⇒ f = 1/P = −10 cm.

    For thin lenses in contact the net power is the algebraic sum of individual powers:

    $P = P_1 + P_2 = (-15) + (+5) = -10\ \text{D}.$

    The equivalent focal length is

    …

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11. CBSE 2019Set ANNUAL1 mark
    Q.Write relation between power of lens and it's focal length.

    ›Reveal solutionSolution

    Power of a lens P = 1/f, with f in metres and P in dioptres.

    The power of a lens measures its ability to converge or diverge light. It is defined as the reciprocal of the focal length:

    P = 1/f

    where f is in metres and P is in dioptre (D).

    • A converging (convex) lens has positive f, so positive power. …

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12. CBSE 2019Set ANNUAL1 mark
    Q.Define first focus of a concave lens.

    ›Reveal solutionSolution

    First focus of a concave lens = the point toward which incident rays must head so that refracted rays become parallel to the axis (a virtual point).

    The first (or object-side) focal point of a lens is defined by the behaviour of rays that emerge parallel to the principal axis.

    For a converging lens it is the point on the axis from which rays diverge to become parallel after refraction. For a concave (diverging) lens, incident rays cannot actually pass through a real focus; instead, the first focus is the point on the principal axis toward which the incident rays must be aimed (converging toward it) so that after refraction they travel parallel to the principal axis.

    …

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