CBSE Class 12-science Answered

the critical angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees. Make particular note that the critical angle is an angle of incidence value. For the water-air boundary, the critical angle is 48.6-degrees. For the crown glass-water boundary, the critical angle is 61.0-degrees. The actual value of the critical angle is dependent upon the combination of materials present on each side of the boundary.

Let's consider two different media - creatively named medium i (incident medium) and medium r (refractive medium). The critical angle is the  that gives a  value of 90-degrees. If this information is substituted into Snell's Law equation, a generic equation for predicting the critical angle can be derived. The derivation is shown below.

n_i • sine() = n_r • sine (90 degrees)

n_i • sine() = n_r

sine() = n_r/n_i

 = sine^-1 (n_r/n_i) = invsine (n_r/n_i)

The critical angle can be calculated by taking the inverse-sine of the ratio of the indices of refraction. The ratio of n_r/n_iis a value less than 1.0. In fact, for the equation to even give a correct answer, the ratio of n_r/n_i must be less than 1.0. Since TIR only occurs if the refractive medium is less dense than the incident medium, the value of n_i must be greater than the value of n_r. If at any time the values for the numerator and denominator become accidentally switched, the critical angle value cannot be calculated. Mathematically, this would involve finding the inverse-sine of a number greater than 1.00 - which is not possible. Physically, this would involve finding the critical angle for a situation in which the light is traveling from the less dense medium into the more dense medium - which again, is not possible.