Refractive index of a prism is `sqrt((7)/(3))` and the angle of prism is `60^@`. The limiting angle of incidence of a ray that will be transmitted thr

Question

Refractive index of a prism is `sqrt((7)/(3))` and the angle of prism is `60^@`. The limiting angle of incidence of a ray that will be transmitted thr

Refractive index of a prism is `sqrt((7)/(3))` and the angle of prism is `60^@`. The limiting angle of incidence of a ray that will be transmitted through the prism is approximately
A. `(pi)/(3)`
B. `(pi)/(6)`
C. `(2pi)/(3)`
D. `(pi)/(2)`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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

Correct Answer - B
Given, refreactive index of prism, `mu=sqrt(7//3)`
and angle of prism, `A=60^(@)`
`"Using" =mu=(sin(A+D_(m))/(2))/("sin"(A)/(2))`
Using angles can be assumed to be small so that sinc of the angle is angle itself.
`i.e. sin (A+D_(m))/(2)=(A+D_(m))/(2) "sin" (A)/(2)=(A)/(2) Rightarrow mu=(A+D_(m))/((2)/(A//2))`
`So, sqrt(7/(3))=(60+D_(m)//(2))/(60//2) or 1.53=(60+D_(m))/(2)xx(1)/(30)`
`D_(m)approx 30^(@)=(pi)/(6)`