I need help please!!!! This is all one problem; it has four parts! I seem to hav

Question

I need help please!!!! This is all one problem; it has four parts! I seem to have many issues with refraction. It would be great if all of the work for each part could be shown! Thank you. :)

The refractive index of a transparent material can be determined by measuring the critical angle when the solid is in air. If c= 41.1° what is the index of refraction of the material?

A light ray strikes this material (from air) at an angle of 33.4° with respect to the normal of the surface. Calculate the angle of the reflected ray (in degrees).

Calculate the angle of the refracted ray (in degrees).

Assume now that the light ray exits the material. It strikes the material-air boundary at an angle of 33.4° with respect to the normal. What is the angle of the refracted ray?

Explanation / Answer

here,

the critical angle , thetac = 41.1 degree

let the refractive index of the material be n

using snell's law

n / 1 = sin(41.1) / sin(90)

n = 0.66

the refractive index of the material is 0.66

when thetai = 33.4 degree

the angle of reflection is equal to the angle of incidence

therefore , the angle of reflection is 33.4 degree with the normal

and let the angle of refration be thetar

using the snell's law

sin(thetar)/sin(thetai) = 1/n

sin(thetar) = sin(33.4) /0.66

thetar = 56.52 degree

the angle of refraction is 56.52 degree

-----------------------------------

when thetai = 33.4 degree

and let the angle of refration be thetar

using the snell's law

sin(thetar)/sin(thetai) = n/1

sin(thetar) = sin(33.4) *0.66

thetar = 21.3 degree degree

the angle of refraction is 21.3 degree

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