A laser beam is traveling through an unknown substance. When itencounters a boun

Question

A laser beam is traveling through an unknown substance. When itencounters a boundary with air, the angle of reflection is22.0° and the angle of refraction is41.0°. (a) What is the index of refraction of thesubstance?

(b) What is the speed of light in the substance?
m/s
(c) At what minimum angle of incidence would the light be totallyinternally reflected?
°
(a) What is the index of refraction of thesubstance?

(b) What is the speed of light in the substance?
m/s
(c) At what minimum angle of incidence would the light be totallyinternally reflected?
°

Explanation / Answer

   angle ofincidence   i   =   angleof reflection                                        =   22.00    angle ofrefraction   r   =   41.00    a.   Snell's lawis      refractive index of airw.r.t. substance   =   sin i / sinr       hence refractive index ofsubstance w.r.t.air      n   =   sinr / sin i       n   =   sin41.00 / sin 22.00             =   1.75             =   1.75    b.   Speed of light in asubstance         v   =   c/ n                                                                         =   3.0* 108 / 1.75                                                                         =   1.71* 108   m/s    c.   critical angle (ic, minimum angle at which total internalreflection occurs) is given by
         sinic   =   1 /n            ic   =   sin-1( 1/ 1.75)                =   34.850

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