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A combination of two prisms, one of flin...

A combination of two prisms, one of flint and other of crown glass produces dispersion without deviation. The angle of flint glass prism is `15^@`. Calculate the angle of crown glass prism and angular separation of red and violet rays on emergence from the spectroscope. (`mu` for crown glass `= 1.52, mu` for flint glass `= 1.65, omega` for crown glass `= 0.02, omega` for flint glass `= 0.03`).

Text Solution

Verified by Experts

Here , `A = 15^(@), A' = ? , omega= 0.03, omega'= 0.02, mu = 1.65, mu' = 1.52`, For no deviation , `delta + delta' = 0`
`(mi-1) A + (mu'-1)A' = 0 implies (1.65-1)15^(@) + (1.52-1)A'=0 implies A' = (-0.65 xx15)/(0.52) = -18.75^(@)`
Negative sign indicates that two prisms must be joined in opposition. Net angular dispersion
`(mu_(v) - mu_(r))A + (mu'_(v) - mu'_(r))A' = omega(mu-1) A + omega'(mu'-1)A' = 0.03 (1.65-1)15^(@) + 0.02(1.52-1) (-18.75^(@))`
=`0.2925 - 0.195 = 0.0975^(@)`
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