The refractive indices $(n)$ of two transparent slabs are 2 and $2 / \sqrt{3}$. They are attached together and placed in a third transparent medium of refractive index $\sqrt{2}$, as shown in the figure. The thickness of the upper slab is $I \mathrm{~cm}$. A monochromatic light ray is incident on the upper slab at $45^{\circ}$. What would be the thickness in cm of the lower slab such that the lateral shift of the ray after passing through both the slabs is zero?

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?

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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