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The refracting angle of a prism is 60^(@...

The refracting angle of a prism is `60^(@)` . It is found that for two different angles of incidence , the deviation produced by the prism is `40^(@)` . If the difference between the two angle of incidence is `10^(@)` . What are their values ?

A

`55^(@) , 45^(@)`

B

`60^(@) , 50^(@)`

C

`65^(@) , 55^(@)`

D

`58^(@) , 48^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
When we get same `delta` , for two angles of incidence , the angle of incidence is either `i` or e because the path of the ray is reversible .
Thus , `i_(1) + e_(1) = A + delta = i_(2) + e_(2) or i+ e = 60^(@) + 40^(@) = 100 " " … (1)`
and `i- e = 10 " " ... (2)`
`therefore 2i= 110 therefore i= 55^(@) and e = 45^(@)`
Similarly when `i = 45^(@) , e = 55^(@)`
Thus the angle are `55^(@) ` and `45^(@)`
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