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Science · 2026 · 4 marks
CBSE 2026 · Region 1 · Set 1 · Q38
Read the following passage and answer the questions given : Lenses can form different types of images depending upon their focal length and position of object. A convex lens can create real, inverted or virtual, erect images, while a concave lens forms only virtual and diminished images. The focal length determines the power of lens. Convex lenses have positive focal length while concave lenses have negative focal length by convention. When lenses are placed together, their combined power is determined by the sum of their individual powers. Ray diagrams help to visualize how light converges or diverges through lens to form an image.(a)A convex lens of focal length $\displaystyle 20$ cm is used to form an image. If an object is placed at $\displaystyle 40$ cm from the lens, what will be the position and nature of image ?(b)Illustrate the formation of image with the help of ray diagram, when the object is placed between the optical centre and principal focus of concave lens.(c)A lens combination consists of a convex lens of focal length $\displaystyle 30$ cm and a concave lens of focal length $\displaystyle 15$ cm placed together. Find the equivalent focal length and power of this lens combination.(ii)Two lenses are placed in contact. One is a concave lens with focal length $\displaystyle 2$ m and the other is a convex lens with focal length $\displaystyle 1.5$ m . What type of lens will the combination behave as (convex or concave) ? Give reason.
Read the following passage and answer the questions given : Lenses can form different types of images depending upon their focal length and position of object. A convex lens can create real, inverted or virtual, erect images, while a concave lens forms only virtual and diminished images. The focal length determines the power of lens. Convex lenses have positive focal length while concave lenses have negative focal length by convention. When lenses are placed together, their combined power is determined by the sum of their individual powers. Ray diagrams help to visualize how light converges or diverges through lens to form an image.
(a)
A convex lens of focal length $\displaystyle 20$ cm is used to form an image. If an object is placed at $\displaystyle 40$ cm from the lens, what will be the position and nature of image ?
(b)
Illustrate the formation of image with the help of ray diagram, when the object is placed between the optical centre and principal focus of concave lens.
(c)
A lens combination consists of a convex lens of focal length $\displaystyle 30$ cm and a concave lens of focal length $\displaystyle 15$ cm placed together. Find the equivalent focal length and power of this lens combination.
(ii)
Two lenses are placed in contact. One is a concave lens with focal length $\displaystyle 2$ m and the other is a convex lens with focal length $\displaystyle 1.5$ m . What type of lens will the combination behave as (convex or concave) ? Give reason.
Marking-scheme solution
(a)
Position - Image will form at $\displaystyle 40$ cm / 2F /C
Nature - Real and inverted
Alternate answer
\[\mathrm{f}=+20 \mathrm{~cm}, \mathrm{u}=-40 \mathrm{~cm}
\]
Using Lens Formula,
\[\begin{array}{l}
\frac{1}{v}-\frac{1}{u}=\frac{1}{f} \\
\frac{1}{v}-\frac{1}{-40}=\frac{1}{20} \\
\frac{1}{v}=\frac{1}{20}+\frac{1}{-40} \\
v=+40 \mathrm{~cm}
\end{array}
\]
Position - $\displaystyle 40$ cm on the other side of the lens
Nature - Real and inverted
(b)
(c)
\[\begin{array}{l}
\mathrm{f}_{1}=30 \mathrm{~cm}=0.3 \mathrm{~m}, \quad \mathrm{f}_{2}=-15 \mathrm{~cm}=-0.15 \mathrm{~m} \\
\mathrm{P}=\frac{1}{\mathrm{f}} \\
\mathrm{P}_{1}=\frac{+1}{0.3} \mathrm{D} ; \mathrm{P}_{2}=\frac{-1}{0.15} \mathrm{D}
\end{array}
\]
Equivalent power, $\displaystyle \mathrm{P}=\mathrm{P}_{1}+\mathrm{P}_{2}$
\[\mathrm{P}=-3.33 \mathrm{D}
\]
Equivalent focal length, $\displaystyle \mathrm{f}=\frac{1}{\mathrm{P}}$
\[\mathrm{f}=\frac{-1}{3.33}=-0.3 \mathrm{~m}=-30 \mathrm{~cm}
\]
(ii)
Combination Lens will behave like convex lens
$\displaystyle \mathrm{f}_{1}=-2 \mathrm{~m}, \mathrm{f}_{2}=1.5 \mathrm{~m}$
\[\begin{array}{l}
\mathrm{P}=\frac{1}{\mathrm{f}} \\
\mathrm{P}_{1}=\frac{-1}{2} \mathrm{D}, \mathrm{P}_{2}=\frac{+1}{1.5} \mathrm{D} \\
\mathrm{P}=\mathrm{P}_{1}+\mathrm{P}_{2} \\
\mathrm{P}=\frac{1}{6} \\
\mathrm{f}=+6 \mathrm{~m}
\end{array}
\]
The focal length of combination is positive.
Alternate answer
Combination Lens will behave like convex lens.
Convex lens - Less ' f ', More ' $\displaystyle \mathrm{P}_{1}$ '
Concave lens - More 'f', Less ' $\displaystyle \mathrm{P}_{2}$ '
Combined Power $\displaystyle =\mathrm{P}_{1}+\mathrm{P}_{2}$, which will be positive.
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CBSE Class 10 Science past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.