CBSE 2025 · Region 7 · Set 1 · Q18 · 2 marks
Using the mirror equation and the formula of magnification, deduce that "the virtual image produced by a convex mirror is always diminished in size and is located between the pole and the focus."A convex lens of focal length $\displaystyle 10$ cm , a concave lens of focal length $\displaystyle 15$ cm and a third lens of unknown focal length are placed coaxially in contact. If the focal length of the combination is +$\displaystyle 12$ cm , find the nature and focal length of the third lens, if all lenses are thin. Will the answer change if the lenses were thick?
Using the mirror equation and the formula of magnification, deduce that "the virtual image produced by a convex mirror is always diminished in size and is located between the pole and the focus."
A convex lens of focal length $\displaystyle 10$ cm , a concave lens of focal length $\displaystyle 15$ cm and a third lens of unknown focal length are placed coaxially in contact. If the focal length of the combination is +$\displaystyle 12$ cm , find the nature and focal length of the third lens, if all lenses are thin. Will the answer change if the lenses were thick?
Marking-scheme solution
Deducing for
(a) Size $\displaystyle 1$
(b) Location of the image produced by convex mirror $\displaystyle 1$
Let, \(\displaystyle \mathrm{u}=\mathrm{nf}\)
From the Mirror formula,
\[\begin{gathered}
\frac{1}{v}+\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}} \\
\frac{1}{v}=\frac{1}{\mathrm{f}}-\frac{1}{\mathrm{u}} \\
=\frac{1}{\mathrm{f}}+\frac{1}{n \mathrm{f}}
\end{gathered}
\]
m is always positive & less than 1.
\[\begin{aligned}
& \frac{1}{\mathrm{f}}=\frac{1}{\mathrm{f}_{1}}+\frac{1}{\mathrm{f}_{2}}+\frac{1}{\mathrm{f}_{3}} \\
& \frac{1}{12}=\frac{1}{10}-\frac{1}{15}+\frac{1}{\mathrm{f}_{3}} \\
& \frac{1}{\mathrm{f}_{3}}=\frac{5-6+4}{60} \\
& \mathrm{f}_{3}=20 \mathrm{~cm}
\end{aligned}
\]
Nature: Convex
Yes
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CBSE Class 12 Physics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.