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An equilateral glass prism (mu = 1.6) is...

An equilateral glass prism `(mu = 1.6)` is immersed in water `(mu = 1.33)`. Calculate the angle of deviation produced for a ray of light incident at `40^@` on one face of the prism.

Text Solution

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For an equilateral glass prism,
`A = 60^(@), .^(a)mu_(g) =1.6` and `.^(a)mu_(w) = 1.33`
`:. .^(a)mu_(g) =(.^(a)mu_(g))/(.^(a)mu_(w)) = (1.6)/(1.33) = 1.203`

For refraction on face `Ab`, Fig.
`i_(1) = 40^(@), r_(1) = ?`
`.^(w)mu_(g) = (sin i_(1))/(sin r_(1)) = 1.203`
`sin r_(1) = (sin i_(1))/(1.203) = (sin 40^(@))/(1.203) = (0.6428)/(1.203) = 0.5343`
`:. r_(1) = 32^(@)18'`
As `r_(1) + r_(2) = A, r_(2) = A - r_(1) = 60^(@) - 32^(@)18'`
`= 27^(@)42'`
Again `.^(w)mu_(g) = (sin i_(2))/(sin r_(2)) = 1.203`
`sin i_(2) = 1.203 sin 27^(@)42' = 1.203 xx 0.4648`
`= 0.5592`
`i_(2) = 34^(@)`
Angle of deviation,
`delta = i_(2) + i_(2) - A = 40^(@) + 34^(@) - 60^(@) = 14^(@)`
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