A point object is placed at a distance of $60 \mathrm{cm}$ from a convex lens of focal length $30 \mathrm{cm}$. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of $40 \mathrm{cm}$ from it, the final image would be formed at a distance of :

Find the value of the angle of emergence from the prism. Refractive index of the glass is $\sqrt{3}$.

A small coin is fixed at the center of the base of an empty cylindrical steel container having radius $R=1 \mathrm{m}$ and height $d=4 \mathrm{m}$. At time $t=0 \mathrm{s}$, the container starts getting filled with water at a flowrate of $Q=0.1 {\mathrm{m}}^3/\mathrm{s}$ without disturbing the coin. Find the approximate time when the coin will first be seen by the observer "$O$" from the height of $H=5.75 \mathrm{m}$ above and $L=1.5 \mathrm{m}$ radially away from the coin as shown in the figure. Refractive index of water is $n=1.33$.

A point object is placed on the axis of a thin convex lens of focal length $0.05 \mathrm{m}$ at a distance of $0.2 \mathrm{m}$ from the lens and its image is formed on the axis. If the object is now made to oscillate along the axis with a small amplitude of $A \mathrm{cm}$, then what is the amplitude of oscillation of the image?

[you may assume, $\frac{1}{1+x}\approx 1-x,$ where $\left.x\ll 1\right]$