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A ray PQ incident on the refracting face BA is refracted in the prism BAC as shown in the figure and emerges from the other refracting face AC as RS such that AQ = AR. If the angle of prism A = 60^(@) and refractive index of material of prism is sqrt(3) , calculate angle theta. |
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Answer» Solution :The angle of the prism is `A = 60^(@)`. It is also given that AQ = AR. THEREFORE, the angles opposite to these two sides are also equal. Now for the triangle AQR, `angleA + angleAQR + angleARQ = 180^(@)` `angleA + angleAQR + angleARQ = 180^(@)` `therefore " " r_(1) = r_(2) = 30^(@) [therefore angleAQO = angleARO = 90^(@)]` `therefore " " r_(1) + r_(2) = 60^(@)` When `r_(1) and r_(2)` are equal, we have i = e. Now, according to Snell.s law, `mu = (sini)/(sinr_(1))` `therefore " " sini = musinr_(1) = sqrt(3) sin30^(@) = (sqrt(3))/(2)` `therefore " " i = 60^(@)` Now, the angle of deviation, `theta = i + e - A = 60^(@) + 60^(@) - 60^(@) = 60^(@)` 
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