Question

Three lenses of focal lengths $+10cm,-10cm$ and $+30cm$ are placed at distance of $30cm$, $35cm$ and $45cm$, respectively from an object. The distance between the object and the image formed is

• A. 100 cm
• B. 75 cm
• C. 30 cm
• D. 45 cm

Answer 1

Answer: (B)

Three lenses of focal length $10,-10$ and $30cm$ is given in figure,

Now, using lens formula, distance of image from lens $A$
$\frac{1}{v_A}-\frac{1}{u_A}=\frac{1}{f_A}$
$\Rightarrow \frac{1}{v_A}-\frac{1}{(-30)}=\frac{1}{+10}$
$\Rightarrow v_A=+15cm$
Similarly, distance of image from lens $B$,
$\frac{1}{v_B}-\frac{1}{(+10)}=-\frac{1}{10}$
$\Rightarrow v_B=\infty$
distance of image from lens $C$,
$\frac{1}{v_c}-\frac{1}{\infty }=\frac{1}{30}$
$\Rightarrow v_c=+30cm$
Hence, the total distance between object and image,
$d_T=d_{0C}+V_C=(30+45)cm=75cm$