A vessel is filled with two different liquids which do not mix. One is 40 cm deep and has refractive index 1.6 and other is 30 cm deep and has refractive index $1 \cdot 5$. The apparent depth of vessel when viewed normally is

An ink mark is made on a piece of paper. A glass slab of thickness ' $t$ ' is placed on it. The ink mark appears to be raised up through a distance ' $x$ ' when viewed at nearly normal incidence. If the refractive index of material of glass slab is ' $\mu$ ' then thickness of glass slab ' $t$ ' is given by

For a light ray to undergo total internal reflection ( $\mathrm{i}=$ angle of incidence, $\mathrm{i}_{\mathrm{c}}=$ critical angle)

When the same monochromatic ray of light travels through glass slab and through water, the number of waves in glass slab of thickness 5 cm is same as in water column of height 6 cm . If refractive index of glass is 1.56 , then refractive index of water is