The ability of a medium to refract light is expressed in terms of its optical density. Optical density has a definite connotation. It is not the same as mass density. On comparing two media, the one with the large refractive index is optically denser medium than the other. The other medium with a lower refractive index is optically rarer. Also the speed of light through a given medium is inversely proportional to its optical density.

(i) Determine the speed of light in diamond if the refractive index of diamond with respect to vacuum is 2.42. Speed of light in vacuum is $3 \times 10^8 m/s$. (1 mark)

(ii) Refractive indices of glass, water and carbon disulphide are 1.5, 1.33 and 1.62 respectively. If a ray of light is incident in these media at the same angle (say $\theta$), then write the increasing order of the angle of refraction in these media. (1 mark)

(iii) (A) The speed of light in glass is $2 \times 10^8 m/s$ and in water is $2.25 \times 10^8 m/s$. (a) Which one of the two is optically denser and why? (b) A ray of light is incident normally at the water-glass interface when it enters a thick glass container filled with water. What will happen to the path of the ray after entering the glass? Give reason. (2 marks)

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(iii) (B) The absolute refractive indices of water and glass are $4/3$ and $3/2$ respectively. If the speed of light in glass is $2 \times 10^8 m/s$, find the speed of light in (i) vacuum and (ii) water. (2 marks)