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Physics · 2025 · 2 marks
Ray Optics and Optical InstrumentsReflection of Light by Spherical Mirrors2 marksApplyvery short answer
CBSE 2025 · Region 7 · Set 1 · Q18
(a) Using the mirror equation and the formula of magnification, deduce that "the virtual image produced by a convex mirror is always diminished in…
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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