A point source is placed at coordinates $(0,1)$ in $xy$ -plane. A ray of light from the source is reflected on a plane mirror placed along the $X$ -axis and perpendicular to the $xy$ -plane. The reflected ray passes through the point $(3,3) .$ What is the path length of the ray from $(0,1)$ to $(3,3)$$?$

A ray of light is incident on a right-angled isosceles prism parallel to its base as shown in the figure. Refractive index of the material of the prism is $\sqrt{2}$. Then, which of the following statement(s) is/are true?

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 $\left.x\ll 1\right]$
 

Two identical equiconvex lenses, each of focal length $f$ are placed side by side in contact with each other with a layer of water in between them as shown in the figure. If refractive index of the material of the lenses is greater than that of water, how the combined focal length $F$ is related to $f ?$