Question

Optical axis of a thin equi-convex lens is the $X-$axis. The coordinate of a point object and its image are ($-20cm,1cm$) and ($25cm,-2cm$) respectively:-

• A. the lens is located at $x=5cm$
• B. the lens is located at $x=-5cm$
• C. the focal length of the lens is $10cm$
• D. the focal length of the lens is $15cm$

Answer 1

Answer: (B), (C)

The correct options are
B the lens is located at $x=-5cm$
C the focal length of the lens is $10cm$

$\begin{array}{c}\text{let the lens be at}(x,0)\\ \begin{array}{cc}{h}_0& =1cm{h}_i=-2c_m\\ \text{magnification}& =\frac{h_i}{h_0}=-\frac{2}{1}=-2\\ & =\frac{v}{u}=-2\end{array}\end{array}$

$\begin{array}{c}u=-D\\ V=45-D\\ \frac{V}{u}=-2\\ \frac{45-D}{-D}=-2\\ D=15\\ \text{So}x=D-20\\ \begin{array}{c}x=15-20\\ x=-5cm\end{array}\\ \text{lens located at}x=-5cm\end{array}$

$\begin{array}{c}u=-15V=30\\ \frac{1}{f}=\frac{1}{v}-\frac{1}{4}\\ \frac{1}{f}=\frac{1}{30}-\frac{1}{-15}\\ \frac{1}{f}=\frac{1}{30}+\frac{2}{30}\\ f=10cm\\ \text{so, B and C}\text{are correct options}\end{array}$