Question

The ability of 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.

1. 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 × 10⁸ m/s. 
2. 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 θ), then write the increasing order of the angle of refraction in these media. 
3. (A) The speed of light in glass is 2 × 10⁸ m/s and is water is 2.25 × 10⁸ m/s.
   (a) Which one of the two 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. 
   OR
   (B) The absolute refractive indices of glass and water are 4/3 and 3/2, respectively. If the speed of light in glass is 2 × 10⁸ m/s, calculate the speed of light in (i) vacuum (ii) water.

Answer 1

(i) Refractive index of diamond,

n = `"Speed of light in vacuum"/"Speed of light in diamond"`

n = `"c"/"v"`

2.42 = `(3xx10^8)/"Speed of light in diamond"`

Speed of light in diamond = `(3xx10^8)/2.42`

= 1.25 × 10⁸ m/s. 

(ii) r_water < r_glass < `"r"_"carbon disulphide"`

(iii) (A) (a) Since the speed of light is greater in water than in glass, glass is optically denser than water. This demonstrates that glass presents a greater barrier to light transmission than water.

(b) After refraction, the light will bend towards normal.

OR

(B) Refractive index of glass, η_g = 4/3

`thereforeeta_g="Speed of light in vacuum"/"Speed of light in glass"`

`4/3="Speed of light in vacuum"/(2xx10^8)`

`"Speed of light in vacuum "=(4xx2xx10^8)/3=2.6xx10^8"m/s"`

`"Refractive index of water,"eta_w=3/2`

`eta_w="Speed of light in vacuum"/"Speed of light in water"`

`3/2=(2.6xx10^8)/"Speed of light in water"`

`"Speed of light in water" = 1.73 xx 10^8 "m/s"`

Because the information provided is wrong, ideally the speed of light in vacuum is 3 × 10⁸ m/s and the speed of light in water is 2.25 × 10⁸ m/s.

The correct solution is

`"Refractive index of glass,"eta_g=3/2`

`"Refractive index of water,"eta_w=4/3`

`"Refractive index of glass,"eta_g="Speed of light in vacuum"/"Speed of light in glass"`

`3/2="Speed of light in vacuum"/(2xx10^8)`

`"Speed of light in vacuum "=(3xx2xx10^8)/2=3xx10^8"m/s"`

`"Refractive index of water, "eta_w=4/3`

`eta_w="Speed of light in vacuum"/"Speed of light in water"`

`4/3=(3xx10^8)/"Speed of light in water"`

`"Speed of light in water "=(3xx3xx10^8)/4`

`"Speed of light in water "=2.25xx10^8"m/s"`