A light wave travels from glass to water. The refractive index for glass and water are $\frac{3}{2}$ and $\frac{4}{3}$, respectively. The value of the critical angle will be

The graph shows how the magnification $m$, produced by a convex thin lens, varies with the image distance $v$. What is the focal length?

A diverging lens of focal length $-10 \mathrm{cm}$ is moving towards right with a velocity $5 \mathrm{m} {\mathrm{s}}^{-1}$. An object placed on the principal axis is moving towards left with a velocity $3 \mathrm{m} {\mathrm{s}}^{-1}$. The velocity of the image at the instant when the lateral magnification produced is $\frac{1}{2}$, is (All velocities are with respect to ground)

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 $\left.x\ll 1\right]$