An object is placed in front of a convex lens. A real inverted image of double its size is formed. When the object is moved closer to the lens by a distance $d$, the image shifts away from the lens by a distance $8 d$ from its previous position. What is the magnitude of the magnification in the final setup?

A thin lens made of material of refractive index $n_l$ forms the image at the position $I$ of a point object held at $O$ on the central axis of the lens, as is shown in the ray diagram below. Consider that the refractive index of the medium is $n_m$ and $n_l>n_m$ for the figure given. Where does the image form when $n_l

What is the maximum angle of incidence $\theta_i$ in the figure for which the ray would satisfy the condition for total internal reflection at the boundary of media of refractive indices $n_1$ and $n_2$, where $n_1>n_2$ ?

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