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Calculate the angle of dispersion betwee...

Calculate the angle of dispersion between red and violet colours produced by a flint glass prism of refracting angle of `60^@` . Given ` mu_v = 1.663 " and " mu_r 1.622` .

Text Solution

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For minimum deviation position,
` mu_(red) = (sin (A+ delta_(red)))/(sin A/2)`
or ` sin ( (A + delta_(red))/(2)) = n_(red)`
`sin A/2 = 1.622 xx 0.5 = 0.811`
` therefore (60 + delta_(red))/(2) = 54^@ 12' `
` delta_(red) = 108^@ 24' - 60^@ = 48^@ 24' `
Similarly `sin ((A+ delta_("violet"))/(2)) = 1.663 xx 0.5`
` = 0.8315 " or " (60^@ + delta_("violet"))/(2) = 56^@ 15' `
` delta_("violet") = 112^@ 30' - 60^@ = 52^@ 30' `
`therefore _("violet") - delta_(red) = (52^@ 30') - (48^@ 24') = 4^@ 6' `
It is not advisable to use the formula `delta_v - delta_r = (mu_v - mu_r) ` in the above solution .
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