Search any question & find its solution
Question:
Answered & Verified by Expert
A bulb is located on a wall. Its image is to be obtained on a parallel with the help of a convex lens. If the distance between parallel walls is ' $d$ ' then the required focal length of the lens placed in between the walls is:
Options:
Solution:
1206 Upvotes
Verified Answer
The correct answer is:
less than or equal to $\frac{d}{4}$
Since $v+u=d \Rightarrow v=d-u$
From lens formula
$$
\begin{aligned}
\frac{1}{f} & =\frac{1}{v}-\frac{1}{u} \\
\Rightarrow \quad \frac{1}{f} & =\frac{1}{d-u}-\frac{1}{-u} \\
& =\frac{d}{(d-u) u} \\
\Rightarrow \quad f & =\frac{d u-u^2}{d} \ldots(\mathrm{i})
\end{aligned}
$$
Differentiating eq. (i) we have
$$
\frac{d f}{d u}=\frac{1}{d}(d-2 u)
$$
for maximum value of $f_1=\frac{d f}{d u}=0$
$$
\begin{aligned}
& \Rightarrow \frac{1}{d}(d-2 u)=0 \Rightarrow d=24 \\
& \Rightarrow u=\frac{d}{2}
\end{aligned}
$$
putting these value in eq. (i)
$$
f=\frac{d}{4}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.