$A$ plane glass plate is placed over various coloured letters (violet,green,yellow,red). Which letter appears to be raised the most?

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness $h$ in terms of the angle of incidence $i$ and angle of refraction $r$,if the glass slab is placed in air medium?

Consider a configuration of $n$ identical units,each consisting of three layers. The first layer is a column of air of height $h=\frac{1}{3} \text{ cm}$,and the second and third layers are of equal thickness $d=\frac{\sqrt{3}-1}{2} \text{ cm}$,and refractive indices $\mu_1=\sqrt{\frac{3}{2}}$ and $\mu_2=\sqrt{3}$,respectively. $A$ light source $O$ is placed on the top of the first unit,as shown in the figure. $A$ ray of light from $O$ is incident on the second layer of the first unit at an angle of $\theta=60^{\circ}$ to the normal. For a specific value of $n$,the ray of light emerges from the bottom of the configuration at a distance $l=\frac{8}{\sqrt{3}} \text{ cm}$,as shown in the figure. The value of $n$ is. . . . .

To a bird in air, a fish in water appears to be at $30 \,cm$ from the surface. If the refractive index of water with respect to air is $\frac{4}{3}$, the real depth of the fish from the surface is: (in $\,cm$)

$A$ plane glass slab is kept over various coloured letters. The letter which appears least raised is

$A$ glass slab is placed over letters of different colors. Which color letter will appear to be raised the least?