total internal reflection between two materials is seen to occur if a critical angle of 60 degrees is exceeded. if the index of refraction of the material that the light is entering is 1.98,find the inndex of refraction of the material in which the light is originating.

Snells Law says that, for the limiting critical reflection angle,

1.98 sin 60 = N2*sin 90 = N2
N2 = 1.715

To find the index of refraction of the material in which the light is originating, we can use the concept of total internal reflection and the critical angle.

The critical angle is the angle of incidence where the refracted angle becomes 90 degrees. When the angle of incidence is greater than the critical angle, total internal reflection occurs.

The relationship between the indices of refraction of two materials and the critical angle is given by Snell's Law:

n1 * sin(critical angle) = n2 * sin(90)

In this case, n1 represents the index of refraction of the material that the light is entering, and n2 represents the index of refraction of the material in which the light is originating.

Given that the critical angle is 60 degrees and the index of refraction of the material that the light is entering (n1) is 1.98, we can substitute these values into the equation:

1.98 * sin(60) = n2 * sin(90)

Now, let's solve for n2:

sin(60) = n2 * sin(90) / 1.98

Using a scientific calculator, evaluate sin(60) ≈ 0.866. Substituting this result, the equation becomes:

0.866 = n2 * 1 / 1.98

Simplifying:

n2 = 0.866 * 1.98 ≈ 1.712

Therefore, the index of refraction of the material in which the light is originating is approximately 1.712.