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A beam of parallel rays is brought to focus by a plano-convex lens. A thin concave lens of the same focal length is joined to the first lens. The effect of this is
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Verified Answer
The correct answer is:
the focus shifts to infinity
The focal length of the combination is given by
$\frac{1}{F}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$
$$
\begin{aligned}
f_{1} &=\text { focal length of plano-convex lens }=f \\
f_{2} &=\text { focal length of concave lens }=-f \\
\therefore \quad \frac{1}{F} &=\frac{1}{f}+\frac{1}{-f}=0 \\
\Rightarrow \quad F &=\infty
\end{aligned}
$$
Hence, focus shifts to infinity.
$\frac{1}{F}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$
$$
\begin{aligned}
f_{1} &=\text { focal length of plano-convex lens }=f \\
f_{2} &=\text { focal length of concave lens }=-f \\
\therefore \quad \frac{1}{F} &=\frac{1}{f}+\frac{1}{-f}=0 \\
\Rightarrow \quad F &=\infty
\end{aligned}
$$
Hence, focus shifts to infinity.
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