A beam of laser light with wavelength 617 nm is directed through a slab of glass

Question

A beam of laser light with wavelength 617 nm is directed through a slab of glass having index of refraction 1.65. For what minimum incident angle would a ray of light undergo total internal reflection? If a layer of water is placed over the glass, what is the minimum angle of incidence on the glass-water interface that will result in total internal reflection at the water-air interface? (The beam of light is directed upward through the slab of glass, through the layer of water, and experiences total internal reflection at the water-air interface on top.)

Explanation / Answer

As it is said, the internal reflection occurs in water-air interface, the critical angle depends on these two refractive index ..

n1 = refractive index of glass ; n2 = refractive index of water ; n3= refractive index of air = 1

t1 = angle of incidence at glass-water interface ; t2 =angle of refraction at glass-water interface or angle of incidence at water-air interface ; t3= angle of refraction at water-air interface

For glass-water interface, use Snell's law,

sin(t1)/sin(t2) = n2/n1   

For water-air interface,

sin(t2)/sin(t3) = n3/n2 or sin(t2)/sin(90) = 1/n2 --> sin(t2) = 1/n2

substitute this in above equation,

sin(t1) = (n2/n1)*(1/n2) = 1/n1

angle = t1= asin(1/1.65) = 37.3 degree

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