A point like object is placed at distance of $$1\,\text{m}$$ in front of a convex lens of focal length $$0.5\,\text{m}$$. A plane mirror is placed at a distance of $$2\,\text{m}$$ behind the lens. The position and nature of the image formed by the system is:

$$\text{First refraction through lens: } u_1 = -1\ \text{m},\ f = +0.5\ \text{m}$$

$$\frac{1}{v_1} - \frac{1}{-1} = \frac{1}{0.5} \implies v_1 = +1\ \text{m}\ (\text{at } I_1)$$

$$\text{Reflection from mirror: } u_2 = -(2 - v_1) = -1\ \text{m} \implies v_2 = +1\ \text{m}\ (\text{at } I_2)$$

$$\text{Second refraction (light moving left): } u_3 = -(2 + v_2) = -3\ \text{m},\ f = +0.5\ \text{m}$$

$$\frac{1}{v_3} - \frac{1}{-3} = \frac{1}{0.5} \implies \frac{1}{v_3} = 2 - \frac{1}{3} = \frac{5}{3} \implies v_3 = +0.6\ \text{m}$$

$$\text{Total distance from mirror} = 2 + v_3 = 2 + 0.6 = 2.6\ \text{m}$$