A ray of light (ray a) in air strikes a flat piece of glass at an angle of phi_0

Question

A ray of light (ray a) in air strikes a flat piece of glass at an angle of phi_0 = 84 degree with respect to the normal, as shown in the figure. The index of refraction of the glass is 1.5. What is the angle theta between the reflected ray (ray b) and refracted ray (ray c) rays? A beam of light traveling in air strikes a slab of transparent material. The incident beam makes an angle of 40 degree the normal, and the refracted beam make an angle of 26 degree with the normal What is the speed of light in the transparent material? (c = 3.0 Times 10^8 m/s) 1.0 Times 10^8 m/s 2.0 Times 10^8 m/s 2.3 Times 10^8 m/s 3.0 Times 10^8 m/s 0.50 Times 10^8 m/s

Explanation / Answer

1. refractive index =sine of incidence angle/sine of refractive angle

1.5=sin(84)/sin(90-theta)

sin(90-theta)=0.9945/1.5

=0.633

taking inverse of it

(90-theta)=sine inverse of 0.633

(90-theta)=39.271

theta=50.72819 degree answer

2.Calculate refractive idex using snell's law

Refractive index =sine of 40/sine of 26

=0.6427/0.4383

=1.466

The speed of light will be =c/refractive index

=3*(10^8)/1.466

=2.046*(10^8)

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