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Prism X deviates red ray through 10^(@) ...

Prism X deviates red ray through `10^(@)` and violet ray through `16^(@)` , while the prism Y deviates red ray through `8^(@)` and violet ray through `14^(@)` , respectively . If `omega_(X)` and `omega_(Y)` are the dispersive powers of X and Y , then

A

`omega_(X) = omega_(Y)`

B

`omega_(X) gt omega_(Y)`

C

`omega_(X) lt omega_(Y)`

D

`omega_(X) = 1.1 (omega_(Y))`

Text Solution

Verified by Experts

The correct Answer is:
C
For the prism `X , delta_(V) = 16^(@) , delta _(R) = 10^(@)`
For the prism `Y , delta_(V) = 14^(@) , delta _(R) = 8^(@)`
For the red and violet colours , for the prism X . The dispersive power,
`omega_(X) = (delta_(V) - delta_(R))/(((delta_(V) - delta_(R))/(2))) = (16^(@) - 10^(@))/(((16^(@) + 10^(@))/(2))) = (6)/(13)`
For the prism Y , `omega_(Y) = (14^(@) - 8^(@))/(((14^(@) + 8^(@))/(2))) = (6)/(11)`
Thus , `omega_(Y) gt omega_(X) or omega_(X) lt omega_(Y)`
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