$A$ plane glass slab is kept over a coloured word '$VIBGYOR$',where the colour of each letter corresponds to the colours in white light. The letter which appears least raised is

Some water is filled in a container of height $30 \, cm$. If it is to appear half-filled to the observer when viewed from the top of the container, the height up to which water should be filled in it is [Refractive index of water $= \frac{4}{3}$] (in $cm$)

When a convex lens is placed above an empty tank,the image of a mark at the bottom of the tank,which is $45 \ cm$ from the lens,is formed $36 \ cm$ above the lens. When a liquid is poured in the tank to a depth of $40 \ cm$,the distance of the image of the mark above the lens is $48 \ cm$. The refractive index of the liquid is

$A$ narrow,paraxial beam of light is converging towards a point $I$ on a screen. $A$ plane parallel plate of glass of thickness $t$ and refractive index $\mu$ is introduced in the path of the beam. The convergence point is shifted by

Each quarter of a vessel of depth $H$ is filled with liquids of the refractive indices $n_1, n_2, n_3$ and $n_4$ from the bottom respectively. The apparent depth of the vessel when looked normally is

In a vessel of $21 \, cm$ depth,up to what height should water be filled so that it appears to be $20\%$ filled when viewed from the top (in $, cm$)? (Given: $\mu_{water} = 4/3$)