The figure shows a ray of light falling normally on the face AB of an equilateral glass prism having a refractive index $3/2$, placed in water of refractive index $4/3$ . Will this ray suffer total internal reflection on striking the face AC? Justify your answer.

A symmetric biconvex lens of the radius of curvature $R$ and made of glass of refractive index $1.5$, is placed on a layer of liquid placed on top of a plane mirror as shown in the figure. An optical needle with its tip on the principal axis of the lens is moved along the axis until its real, inverted image coincides with the needle itself. The distance of the needle from the lens is measured to be $x$. On removing the liquid layer and repeating the experiment, the distance is found to be $y$. Obtain the expression for the refractive index of the liquid in terms of $x$ and $y$.

Draw a labelled ray diagram of an astronomical telescope in the near point adjustment position.

A giant refracting telescope at an observatory has an objective lens of focal length $15 \mathrm{m}$ and an eyepiece of focal length $1.0 \mathrm{cm}$. If this telescope is used to view the Moon, find the diameter of the image of the Moon formed by the objective lens. The diameter of the Moon is $3.48\times {10}^6 \mathrm{m}$, and the radius of the lunar orbit is $3.8\times {10}^8 \mathrm{m}$.

Three lenses of focal length $+10 cm, -10 cm, +30 cm$ are arranged coaxially as in the figure given below. Find the position of the final image formed by the combination.