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Determine the angle of flint glass prism...

Determine the angle of flint glass prism, which should be combined with a crown glass prism of `5^@` so as to give dispersion, but no deviation. Given for crown glass, `mu_v = 1.523, mu_r 1.515` For flint glass, `mu_v' = 1.688, mu_r' = 1.650`.

Text Solution

Verified by Experts

The correct Answer is:
`- 3.88^@`
`A = 5^@, A' = ?, mu_v = 1.523, mu_r = 1.515`
`mu'_v = 1.688, mu'_r = 1.650`
`mu = (mu_v + mu_r)/(2) = (1.523 + 1.515)/(2) = 1.519`
`mu' = (mu_v' + mu_r')/(2) = (1.688 + 1.650)/(2) = 1.669`
For no deviation, `delta + delta' = 0`
`(mu - 1) A + (mu' - 1) A' = 0`
`A' = (-(mu - 1)A)/((mu' - 1)) = (-(1.519 - 1))/((1.669 - 1)) = (-0.519 xx 5)/(0.669)`
=`-3.88^@`
Negative sign indicates that prisms must be joined in opposition.
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Knowledge Check

  • The net angular dispersion produced without deviation for crown glass (mu = 1.56) and flint glass ( mu = 1.7) is

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