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A crown glass prism of refracting angle ...

A crown glass prism of refracting angle `A= 6^@` is to be achromatised for red and blue light using a flint glass prism. Find the angle of flint glass prism (A') and also, the mean deviation from the following data : `mu_b=1.531` `mu_r=1.520` `mu'_b=1.684` `mu'_r=1.662`

Text Solution

Verified by Experts

For achromatic combination,
`(mu_(b) - mu_(r ))A = -(mu'_(b) - mu'_(r ))A'`
`A' = -((mu_(b) - mu_(r ))A)/((mu'_(b) - mu'_(r ))) = -((1.531 - 1.520)6)/((1.684 - 1.662))`
`= -(0.011 xx 6)/(0.022) = - 3^(@)`
Mean deviation `= (mu - 1)A + (mu' - 1)A'`
`= A((1.531 + 1.520)/(2) - 1)xx ((1.662 + 1.684)/(2) - 1)`
`= 6^(@)(1.5255 -1) - 3^(@)(1.673 -1) xx ( -3)`
`= 3.513 - 2.019 = 1.134^(@)`
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