Question

If the optic axis of convex and concave lenses are separated by a distance $5mm$ as shown in the figure. Find, the co-ordinate of the final image formed by the combination if parallel beam of light is incident on lens. Origin is at the optical centre of convex lens

• A. $(25 cm, 0.5 cm)
• B. $(25 cm, 0.25 cm)
• C. $(25 cm,- 0.5 cm)
• D. $(25 cm,- 0.25 cm)

Answer 1

The correct option is B $(25cm,0.25cm)$ $$\begin{array}{c}\text{The image from convex lens is formed}20cms\\ \text{away from it meang}u\text{for concave lens}\\ \to (30-20)=10cm\text{\& object height}=Smm\end{array}$$ $

${}_0^{\circ }$ by lens formula$\Rightarrow \frac{1}{f}=\frac{1}{(-10)}=\frac{1}{(-10)}$

$\frac{1}{v}=\frac{-2}{10}\Rightarrow v=-5cm]-ve$ here means object is at left of concave lens. $

x$-coordinate$\Rightarrow \quad 20+5 \Rightarrow \therefore 25 \mathrm{~cm}$

$\begin{array}{cc}\text{For}y-\text{coordinate}\to \frac{h_i}{h_0}& =\frac{v}{u}\Rightarrow \frac{h_i}{S_{mm}}=\frac{-5\times {10}^{\circ }mm}{-10\times 10mm}\\ h_0=25mm& {}^{}\end{array}$

$\therefore$ hi= $0.25cm$ ie $y$ -coordinate

Hence option $B$ ' is correct.