A ray of light passing through an equilateral traingular glass prism from air undergoes minimum deviation when angle of incidence is `3//4` th of the

Question

A ray of light passing through an equilateral traingular glass prism from air undergoes minimum deviation when angle of incidence is `3//4` th of the

A ray of light passing through an equilateral traingular glass prism from air undergoes minimum deviation when angle of incidence is `3//4` th of the angle of prism. Calculate the speed of light in the prism.

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Here `A=60^(@)`
and `i=(3)/(4)` of `A=(3)/(4)xx60=45^(@)`
Using prism formula, we have
`mu=sin((A+delta_(m))/(2))/sin((A)/(2)) =(sin i)/sin((A)/(2)) [becausei=(A+delta_(m))/(2)]`
But `mu=(C)/(V)`
`therefore (C)/(V)=(sin i)/(sin A//2)`
`(3xx10^(8))/(V)=(sin 45^(@))/(sin60^(@)//2)`
`therefore V(3xx10^(8)xx(1)/2)/(1/(sqrt2))`
`thereforeV=1.5xx1.41xx10^(8)=2.115xx10^(8)m//s`