If minimum deviation = `30^(@)`, then speed of light in shown prism will be

Options

A. `3/sqrt(2)xx10^(8)m//s`
B. `1/sqrt(2) xx 10^(8)m//s`
C. `2/sqrt(3) xx 10^(8)m//s`
D. `(2KAepsilon_(0))/((K^(2)+1)d)`

Answer

A

Explanation

Given, `A = 60^(@)`, `delta_(m)=30^(@)`
According to prism formula,
`mu=(sin((A+delta_(m))/2))/sin(A/2)`
or `mu = (sin(60^(@)+30^(@))/2)=(sin45^(@))/(sin30^(@))`
or `mu = sqrt(2)`
`therefore mu=("Speed of light in air(c)")/("Speed of light in prism(v)")`
`v= c/mu = (3 xx 10^(8))/sqrt(2) = 3/sqrt(2) xx 10^(8)` `m/s`