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The refractive indices of the crown glass for blue and red light are 1.51 and 1.49 resp. and those of flint glass are 1.77 and 1.73 respectively. Two isoscles prisms, one of crown glass and other of flint glass are combined to produce dispersion withoutdeviation. If angle of crown glass prism is 6^(@), what should be the angle of other prism ? Also calculatenet dispersion of the combination. |
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Answer» Solution :Here, for crown glass, PRISM, `mu_(b) = 1.51, mu_(r) = 1.49, A = 6^(@)` and for flint glass prism, `mu'_(b) = 1.77 and mu'_(r ) = 1.73, A' = ?` Now, `mu = (mu_(b) + mu_(r ))/(2) = (1.51 + 1.49)/(2) = 1.50`, and`mu' = (mu'_(b) + mu'_(r ))/(2) = (1.77 + 1.73)/(2) = 1.75` For no deviation, the CONDITIONS is `delta + delta' = 0` `(mu - 1) A + (mu' - 1) A' = 0` `:.A' = (-(mu - 1)A)/((mu' - 1)) = (-(1.50 -1)6^(@))/((1.75 - 1))` `= (-0.50 XX 6^(@))/(0.75) = -4^(@)` Negative sign implies that the two prisms must be COMBINED in opposition. NET dispersion `= (mu_(b) - mu_(r ))A + (mu'_(b) - mu'_(r))A'` `= (1.51 - 1.49) 6^(@) + (1.77 - 1.73)(- 4)` `= 0.02 xx 6 + 0.04 (- 4)` `= 0.12 - 0.16 = - 0.04^(@)` |
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