please answer completely and correctly. thank you. A beam of laser light with wa

Question

please answer completely and correctly. thank you.

A beam of laser light with wavelength 612 nm is directed through a slab of glass having index of refraction 1.5. 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

a)using snell's law

here,for total internal reflection,

as light goes from glass(n=1.5) to air(n=1)

=>1.5*sin (critical angle)=1*sin (90)

=>sin (critical angle)=(2/3)

=>critical angle=41.81 degree

b)

as light goes from glass(n=1.5) to water(n=1.333),then from water to air(n=1)

using snell's law, for each of the boudary layer,

let angle of incidence on the glass water boundary be i

and angle of reflection be r

=>1.5*sin (i)=1.333*sin(r) ---(1)

sin(r)*1.333=1*sin (90) ---(2) [angle of incidence for water glass boundary comes out to be same as r by geometry]

=>1.5*sin (i)=1*sin (90)

=>sin (i)=(2/3)

=>i=41.81 degree

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