Noting down the refractive index of these medium, we have

For kerosene, refractive index, n = 1.44
For turpentine oil, refractive index, n = 1.47
For water, refractive index, n = 1.33 

Since water has lowest refractive index, so light travels fastest in this optically rarer medium than kerosene and turpentine oil.

Refractive index of diamond is 2.42 implies that the ratio of the speed of light in air to that in the medium diamond is 2.42. 

Refraction through a rectangular glass slab:

Consider a rectangular glass slab PQRS, as shown in figure below. On the face PQ, a ray AB is incident at an angle of incidence i₁. It bends towards the normal, on entering the glass slab, and travels along BC inclined at an angle of refraction r₁. The refracted ray BC is incident on the face SR at an angle of incidence i₂. The emergent ray CD bends away from the normal at an angle of refraction r₂. 

Now, using Snell’s law, we have
Refraction from air to glass at face PQ, 

                      $\frac{\sin {\mathrm{i}}_1}{\sin {\mathrm{r}}_1} = \frac{{\mathrm{n}}_{\mathrm{g}}}{{\mathrm{n}}_{\mathrm{a}}}$                  ...(1) 

where, 
n_a is the refractive index of sir and
n_g is the refractive index of glass. 


 
Fig. Refraction through a glass slab

Using Snell’s law for refraction from glass to air at face SR, we have 

                 $\frac{\sin {\mathrm{i}}_2}{\sin {\mathrm{r}}_2} = \frac{{\mathrm{n}}_{\mathrm{a}}}{{\mathrm{n}}_{\mathrm{g}}}$ 

But                   ${\mathrm{i}}_2 = {\mathrm{r}}_1,$

Therefore,
                     $\frac{\sin {\mathrm{r}}_1}{\sin {\mathrm{r}}_2} = \frac{{\mathrm{n}}_{\mathrm{a}}}{{\mathrm{n}}_{\mathrm{g}}}$                    ...(2) 

Multiplying equations (1) and (2), we get 

                     $\frac{\sin {\mathrm{i}}_1}{\sin {\mathrm{r}}_1}\times \frac{\sin {\mathrm{r}}_1}{\sin {\mathrm{r}}_2} = 1$ 

$\Rightarrow$                 $\sin {\mathrm{i}}_1 = \sin {\mathrm{r}}_2$ 

i.e.,                   ${\mathrm{i}}_1 = {\mathrm{r}}_2$ 

Thus, the emergent ray CD is parallel to the incident ray AB, but it has been laterally displaced by a perpendicular distance CN with respect to the incident ray. This lateral shift in the path of light on emerging from a medium with parallel faces is called lateral displacement.

It is found that the lateral displacement is directly proportional to the thickness of the glass slab.

Lateral displacement of an emergent ray depends on: 

(i) Angle of incidence,
(ii) Thickness of the glass slab, and 
(iii) Refractive index of the slab material.