Question
Thu May 24, 2012 By: Aayusha Maharana

Critical angle for glass is 42degree.Would this value change if a piece of glass is immersed in water?Explain. A similar doubt is - A ray of light is travelling from diamond to glass.Calculate the valueof criticalangle for the ray,if the refractive index of glass is 1.51 & that of diamond 2.47 . PLEASE PROVIDE ME SOLUTIONS TO THE ABOBE QUESTIONS & CLARIFY MY CONFUSIONS.

Expert Reply
Fri May 25, 2012

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.

ni *• sine() = nr • sine ()

ni • sine() = nr • sine (90 degrees)

ni • sine() = nr

sine() = nr/ni

 = sine-1 (nr/ni) = invsine (nr/ni)

The critical angle can be calculated by taking the inverse-sine of the ratio of the indices of refraction. The ratio of nr/niis a value less than 1.0. In fact, for the equation to even give a correct answer, the ratio of nr/ni must be less than 1.0. Since TIR only occurs if the refractive medium is less dense than the incident medium, the value of nmust be greater than the value of nr. 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.

 If light is travelling from diamond to glass then critical angle will be 
 = inverse (sin (1.51/ 2.47)) 
Tue February 07, 2017

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