Question

Three lenses of focal lengths $+10\, cm ,-10\, cm$ and $+30\, cm$ are placed at distance of $30\, cm$, $35\, cm$ and $45\, cm$, 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 $30\, cm$ is given in figure,

Now, using lens formula, distance of image from lens $A$
$\frac{1}{v_{A}}-\frac{1}{u_{A}}=\frac{1}{f_{A}}$
$\Rightarrow \frac{1}{v_{A}}-\frac{1}{(-30)}=\frac{1}{+10}$
$\Rightarrow v_{A}=+15\, cm$
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 $C$,
$\frac{1}{v_{c}}-\frac{1}{\infty}=\frac{1}{30}$
$\Rightarrow v_{c}=+30\, cm$
Hence, the total distance between object and image,
$d_{T}=d_{0 C}+V_{C}=(30+45)\, cm =75\, cm$