question_answer

(a) State the laws of refraction of light. Explain the term absolute refractive index of a medium and write an expression to relate it with the speed of light in vacuum.

(b) The absolute refractive indices of two media 'A' and 'B' are 2.0 and 1.5 respectively. If the speed of light in medium 'B' is \[2\times {{10}^{8}}\,m/s,\] calculate the speed of light in:

(i) vacuum,

(ii) medium 'A'

 

Answer:

(a) Laws of refraction of light:

(i) Incident ray travelling from one medium to         another, bend in such a way that the incident ray, refracted ray and the normal ray, at the point of incidence, all lie in the same plane.

(ii) The ratio of sine of angle of incidence to the sine of angle of refraction is constant for a given pair of media.

Absolute refractive index of a medium is the ratio of \[\sin z\] to \[\sin r\].

\[\text{Absolute refractive index=}\frac{\text{Speed of light of vacuum}}{\text{Speed of light in medium}}\]

(b) Given: \[{{n}_{A}}=2.0,\,{{n}_{B}}=1.5,\] speed of light in medium \[B=2\times {{10}^{8}}\,m/s\]

(i) \[{{n}_{B}}=\frac{c}{\text{Speed of light in a medium} ({{\upsilon }_{B}})}=\frac{c}{{{\upsilon }_{B}}}\]

\[c={{n}_{B}}\times {{\upsilon }_{B}}=1.5\times 2\times \mathrm{ }{{10}^{8}}=3\times \mathrm{ }{{10}^{8}}m/s\]

(ii) \[{{n}_{A}}=\frac{c}{{{\upsilon }_{A}}}\]

\[{{\upsilon }_{A}}=\frac{c}{{{n}_{A}}}=\frac{3\times {{10}^{8}}}{2}=1.5\times {{10}^{8}}m/s\text{  }\]