TeXes Science Practice Test

What is the critical angle when light moves from a medium with a higher refractive index to a lower refractive index?

1. tan-1(n2/n1)

2. sin-1(n2/n1)

3. cos-1(n2/n1)

4. cot-1(n2/n1)

The correct answer is: sin-1(n2/n1)

The critical angle is defined in the context of light traveling from a medium with a higher refractive index to one with a lower refractive index. When this occurs, total internal reflection can take place if the angle of incidence exceeds the critical angle. The relationship that defines the critical angle is based on Snell's Law, which describes how light bends when it passes between different media. In this case, the critical angle is determined by using the sine function. When light passes from a denser medium (with a higher refractive index, n1) to a less dense medium (with a lower refractive index, n2), the critical angle can be calculated with the formula: Critical Angle = sin⁻¹(n2/n1) This relationship holds true because the sine of the critical angle corresponds to the ratio of the refractive indices of the two media. Hence, using the inverse sine function, we find that the critical angle can be expressed as sin⁻¹(n2/n1), which clearly corresponds to the answer provided. The application of other trigonometric functions such as tangent, cosine, or cotangent does not accurately capture the relationship required to determine the critical angle in this context. Therefore, the correct formulation specifically features the sine