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Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is mu, a ray, incident at an angle theta, on the face AB would get transmitted through the face AC pf the prism provided. |
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Answer» `THETA gt SIN^-1 [mu sin (A-sin-1((1)/(mu)))]`  For TRANSMISSION, `r_2lt i_c` (Critical ANGLE) `thereforeA-r_1 lt i_c``(because r_1+r_2=A)` `thereforesin(A-r_1) lt sini_c` `therefore sin(A-r_1) lt (1)/(mu)``(because sini_c=1/mu)` `therefore A-r_1 lt sin^(-1)(1/mu)` `thereforer_1 gt A-sin^(-1)(1/mu)` `thereforesinr_1 gt sin[A-sin^(-1)(1/mu)](because sin theta=mu sin r_1)` `therefore(sin theta)/(mu) gt sin[A-sin^(-1)((1)/(mu))]` `therefore sin theta gt mu sin(A-sin^(-1)""(1)/(mu))` `therefore theta gt sin^(-1)(musin(A-sin^(-1)""(1)/(mu)))` |
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