As an aid in working this problem, consult Concept Simulation 26.1 . A ray of li

Question

As an aid in working this problem, consult Concept Simulation 26.1.

A ray of light is traveling in glass and strikes a glass/liquidinterface. The angle of incidence is 57.0°, and the index ofrefraction of glass is n = 1.50. (a) What must be the index of refraction of theliquid such that the direction of the light entering the liquid isnot changed?
1

(b) What is the largest index of refraction that the liquid canhave, such that none of the light is transmitted into the liquidand all of it is reflected back into the glass?
2

Section 26.3 Total InternalReflection
(a) What must be the index of refraction of theliquid such that the direction of the light entering the liquid isnot changed?
1

(b) What is the largest index of refraction that the liquid canhave, such that none of the light is transmitted into the liquidand all of it is reflected back into the glass?
2
Section 26.3 Total InternalReflection

Explanation / Answer

(a)    the index of refractionn2 of the liquid must match that of the glass, orn2 = 1.5 (b)    when none of the light is transmitted intothe liquid, the angle of incidence must be equal to or    greater than the critical angle    critical angle c isgiven by    sin c = n2/ n1     n2 =n1 sin c         = (1.50)sin 57.0°         =1.25    If n2 were larger than1.25    the critical angle would also be larger, andlight would be transmitted from the glass into the    liquid    so n2 = 1.25 representsthe largest index of refraction of the liquid such that none of thelight is     transmitted into the liquid         = (1.50)sin 57.0°         =1.25    If n2 were larger than1.25    the critical angle would also be larger, andlight would be transmitted from the glass into the    liquid    so n2 = 1.25 representsthe largest index of refraction of the liquid such that none of thelight is     transmitted into the liquid

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