Geometrical Optics

Let $V_1$ be the image distance from the lens. Lens formula is $\frac{1}{v}-\frac{1}{u}$ = $\frac{1}{f}$ That is, $\frac{1}{v_1}-\frac{1}{-30}$ = $\frac{1}{15}$ Therefore, $v_1$ = 30 cm. For a plane mirror, the object distance is 20 cm. Therefore, Image distance = 20 cm (Image $I_2$) Final image $I_3$ is formed after refraction from the lens for which $I_2$ acts as an object. The distance of $I_2$ from the lens is 10 cm. Therefore, $\frac{1}{v_3}-\frac{1}{10}$ = $\frac{1}{15}$ ⇒ $\frac{1}{v_3}$ = $\frac{1}{10}+\frac{1}{15}$ = $\frac{5}{30}$ ⇒ $v_3$ = 6 cm. The image is real and at a distance 10 + 6 = 16 cm.