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Good afternoon sir. Answer is 3rd option. Explain it sir.

Good afternoon sir.
Answer is 3rd option.
Explain it sir.

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1 Answers

Arun
25758 Points
4 years ago
let the refractive index be RI 
angle of from air to glass slab incidence = 45 degrees. 
let R1 be the angle of refraction 
sin(45 deg)/sin(R1) = Ri 
sin(R1) = sin(45 deg)/(Ri) 
angle of incidence of the ray on the vertical face of the slab as it travels through it is (90 degrees - R1) 
sin(90)/sin(90 deg -R1) = Ri (here angle of refraction should be 90 degrees because we need total internal reflection) 
1/cos(R1) = Ri 
cos(R1) = 1/Ri 

using sin square theta + cos Square theta = 1, we have square(sin(45 deg)/Ri) + square(1/Ri) = 1 
square(1/(sqrt(2)*Ri)) + square(1/Ri) = 1 
1/(2*square(Ri) + 1/square(Ri) = 1 
=3/(2*square(Ri) ) = 1 
square(Ri) = 3/2 Hence Ri = sqrt(3/2) 

 

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