An object $AB$ is placed $15$ cm on the left of a convex lens $P$ of focal length $10$ cm. Another convex lens $Q$ is now placed $15$ cm right of lens $P$. If the focal length of lens $Q$ is $15$ cm, the final image is ______.
Answer: (B) real, formed at $7.5$ cm right of lens $Q$, with a size same as that of $AB$
Concept. Separated lenses: the image formed by P is the object for Q (here a virtual object, since the light converges towards a point beyond Q). Total magnification $m=m_1m_2$.
Step 1. Lens P. $u=-15$, $f=10$: $\dfrac1v=\dfrac1{10}-\dfrac1{15}=\dfrac1{30}$, $v=30$ cm; $m_1=\dfrac{30}{-15}=-2$.
Step 2. Lens Q. This image is $30-15=15$ cm beyond Q: $u=+15$, $f=15$: $\dfrac1v=\dfrac1{15}+\dfrac1{15}$, $v=7.5$ cm; $m_2=\dfrac{7.5}{15}=\dfrac12$.
Step 3. Final image. Real, $7.5$ cm right of Q, $m=-1$: same size (inverted).
Answer. Option B.
Solution by Sreeraj P, M.Sc Physics
