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The dispersion produced by an equilatera...

The dispersion produced by an equilateral prism of flint- glass is `2.16^(@)` and that produced by an equilateral prism of crown glass is `1.08^(@)` . What should be the angle of a crown glass , which will produce an achromatic combination with a flint-glass prism of refracting angle `30^(@)` ?

A

`45^(@)`

B

`30^(@)`

C

`60^(@)`

D

`75^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
For flint glass , dispersion `= A (n_(v) - n_(R))`
`therefore 2.16^(@) = 60 (n_(v) - n_(R))`
`therefore n_(v) - n_(R) = ((2.16))/((60))`
For crown glass , `1.08 - 60 (n'_(v) - n'_(R)) therefore n_(v) - n_(R) = (1.08)/(60)`
In achromatic combination of flint and crown glass prisms , we get deviation without dispersion .
`A_(1) (n_(v) - n_(R)) = A_(2) (n_(v) - n_(R))`
`therefore A_(2) = (A_(1) (n_(v) - n_(R)))/(n_(v) - n_(R)) = ([30 ((2.16)/(60))])/((1.08)/(60))`
`therefore A_(2) = (2.16)/(2) xx (60)/(1.08) = 60^(@)`
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