Competitive Thinking

How much water should be filled in a container $21 \mathrm{cm}$ in height, so that it appears half filled when viewed from the top of the container?

[given that, ${}_a\mu _w=\frac{4}{3}$]

The angle of a prism is $A$. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2A$ on the first surface returns through the same path after suffering reflection at the silvered surface. The refractive index $\mu$, of the prism is

The refractive index of the material of a prism is $\sqrt{2}$ and the angle of the prism is $30°$. One of the two refracting surfaces of the prism is made a mirror inwards, by a silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is:

When a glass prism of refracting angle $60°$ is immersed in a liquid, its angle of minimum deviation is $30°$. The critical angle of glass prism with respect to the liquid medium is

A beam of light consisting of red, green and blue colours is incident on a right-angled prism. The refractive indices of the material of the prism for the above red, green and blue wavelengths are $1.39,1.44$ and $1.47$, respectively.

A ray falls on a prism $ABC, \left(AB=BC\right)$ and travels as shown in the figure. The minimum refractive index of the material of the prism should be

Assertion: By roughening the surface of a glass sheet its transparency can be reduced.

Reason: Glass sheet with rough surface absorbs more light.

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