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A ray of light passes through an equilateral glass prism such that the angle of incidence is equal to the angle of emergence. The angle of emergence is 3/4 times the angle of prism. Calculate the refractive index of the glass prism.

Answer»

Solution :Since the angle of incidence is equal to angle of emergence therefore the ray of LIGHT passes symmetrically through the prism. So, the prism is in minimum DEVIATION position. Now, `A + delta_m = i + e `
` delta_m = e + e - A = 2 (3/4 A) -A`
` = 3/2 A - A = A/2 = (60^@)/(2)= 30^@`
` n_(21) = (sin ((A+ delta_m)/(2)))/(sin (A/2))= (sin ((60^@ + 30^@)/(2)))/(sin (60^@)/(2))`
` = (sin 45^@)/(sin 30^@) =(1)/(sqrt2) xx 2/1 = SQRT 2`= 1.414


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