A convex lens of focal length $20$ cm and a concave mirror of focal length $10$ cm are placed coaxially $50$ cm apart. An object is placed $30$ cm in front of the lens (on the side away from the mirror). Find the distance, in cm, of the image formed by the mirror from the mirror.
Numerical value type. Enter your answer.
Answer: 5
Lens: $\dfrac{1}{v} = \dfrac{1}{20} - \dfrac{1}{30} = \dfrac{1}{60}$, so $v = 60$ cm: $10$ cm beyond the mirror, which acts as a virtual object for it.
Mirror (distances from the mirror, towards the lens positive for real): the converging rays would meet $10$ cm behind it, $u = +10$, $f = -10$:
$$\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = -\frac{1}{10} - \frac{1}{10} = -\frac{1}{5} \;\Rightarrow\; v = -5\ \text{cm}$$
The image is real, $5$ cm in front of the mirror.
Solution by Sreeraj P, M.Sc Physics