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A parallel beam of rays of width 20 cm passing through a glass slab makes an angle phi=60^(@) with its plane surface. If the beam emerges into air from this surface then calculate the width of emergent beam. Refractive index of glass = 1.8. |
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Answer» Solution :The width of the beam of parallel RAYS = AB = 20 CM and the width of the beam of emergent rays in AIR = CD. From Fig. 2.13, I = `30^(@)` `therefore "" g^(mu)a = (SIN30^(@))/(sinr)` `or, "" sinr = (1)/(2) * (1)/(g^(mu)a) = (a^(mu)g)/(2)` `(1.8)/(2) = 0.9` `"From the figure" , angleBAC = 30^(@) and angleACD = r` `Now, cos 30^(@) = (AB)/(AC), cosr = (CD)/(AC)` `(cos 30^(@))/(cosr) = (AB)/(AC)` `or, "" CD = (ABcosr)/(cos30^(@)) = (20sqrt(1-sin^(2)r))/(sqrt(3/2))= (40)/(sqrt3) sqrt(1-0.81)` `= (40)/(sqrt3) xx sqrt(0.19) = 10.064 cm` 
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