Ray Optics And Optical Instruments Ques 1
1. An equiconvex lens is cut into two halves along (i) $X O X^{\prime}$ and (ii) $Y O Y^{\prime}$ as shown in the figure. Let $f, f^{\prime}, f^{\prime \prime}$ be the focal lengths of the complete lens, of each half in case (i), and of each half in case (ii), respectively.
Choose the correct statement from the following
[2003]
(a) $f^{\prime}=2 f, f^{\prime \prime}=2 f$
(b) $f^{\prime}=f, f^{\prime \prime}=2 f$
(c) $f^{\prime}=2 f, f^{\prime \prime}=f$
(d) $f^{\prime}=f, f^{\prime \prime}=f$
Show Answer
Answer:
Correct Answer: 1.(b)
Solution: (b)
$\frac{1}{f}=(1-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$
In this case, $R_1$ and $R_2$ are unchanged So, $f$ will remain unchanged for both pieces of the lens
$ \begin{aligned} & \therefore f=f^{\prime} \\ & \frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2} \end{aligned} $
This is combination of two lenses of equal focal lengths
$ \therefore \frac{1}{f}=\frac{1}{f^n}+\frac{1}{f^n}=\frac{2}{f^n} \Rightarrow f^n=2 f \text {. } $
A symmetric lens is cut along optical axis in two equal parts. Intensity of image formed by each part will be same as that of complete lens. Focal length is double the original for each part.
BETA
