Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in m…

Question

Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are 2.4 10^8 m/s and 2.7 10^8 m/s, respectively, then the value of critical angle is :

Accepted Answer

Correct answer: D. (d) The refractive index of a medium is inversely proportional to the speed of light in that medium, given by n= cv. For light travelling from medium A to medium B, the critical angle _c is defined when light travels from a denser to a rarer medium. Given speeds are v_A=2.4 10^8 m/s and v_B=2.7 10^8 m/s. The refractive indices are n_A= cv_A and n_B= cv_B. The critical angle _c is given by sin _c= n_Bn_A= v_Av_B. Substituting the values: sin _c= 2.4 10^82.7 10^8= 2427= 89. To find the value in terms of tan^-1, we use the trigonometric identity for a right-angled triangle where perpendicular p=8 and hypotenuse h=9. The base b= h^2-p^2= 9^2-8^2= 81-64= 17. Thus, tan ⁡ _c= pb= 8 17. Therefore, _c= tan^-1 ⁡ ( 8 17 ).

Solution

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