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For right-angled prism, ray-1 is the inc...

For right-angled prism, ray-1 is the incident ri and ray-2 is the emergent ray as shown in the figure. Refractive index of the prism is .........

A

`(1)/(sqrt2)`

B

`(sqrt3)/(2)`

C

`(2)/(sqrt3)`

D

`sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
B, D
As shown in figure, ray-1 inciding at point De surface AB in prism experiences total interna reflection.
`therefore` At point D, angle of incidence formed with perpendicular MN on surface AB is equal to critical angle C = `45^@`
`n=(1)/(sinC)=(1)/(sin45^@)=(1)/(0.7071)=1.414=sqrt2`
It is clear from the figure that ray experience: total internal reflection at points D and E. A these points value of angle of incidence is `45^@`
`therefore45^@ gt C` (critical angle)
`implies sin 45^@ gt sin Cimplies (1)/(sqrt2) gt 1/n implies n ge sqrt2`
Out of given option for `n ge sqrt2,n=sqrt2`
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