Light traveling from water to a gemstone strikes the surface at an angle of 80.0º and has an angle of refraction of 15.2º . (a) What is the speed of light in the gemstone? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?


  1. Answer:


    The the speed of light in the gemstone is  v= 0.599*10^8 m/s


    The unreasonable thing about this is that the speed of ligth in the gemstone is too low

    the speed is 19% of the speed of light  which is very low


    One main unreasonable or inconsistent factor is that the assumption that the  differnce between the angle of incidence and angle of refraction is  very large


      From the question we are told that

           The  angle of incidence  i = 80^o

            The angle of refraction  r = 15.2^o

    From Snell’s law we have ,

          n_1 sin \theta_1 = n_2 sin \theta_2

        Where n_1 is the refractive index of the first medium (water) with a constant value  of  n_1 = 1..333

                    n_2  is the refractive index of the second medium (gem stone)

                     \theta_1 is the angle between  the beam and perpendicular surface of the first medium

                   \theta_2  is the angle  between the beam an the perpendicular surface of the second medium

          Making  the n_2 the subject of the formula

                           n_2 = n_1 \frac{sin \theta_1}{sin \theta_2}

                               = (1.333)(\frac{sin (80.0)}{sin  15.2} )

                               = 5.007

     Generally refractive index of a material  is mathematically represented

                          n = \frac{c}{v}

     Where c is the speed light

                   v is the speed of light  observed in a medium

     Making v the subject

                v = \frac{c}{n}

     substituting value for gem stone

              v  =  \frac{3.0*10^8}{5.007}

                  v= 0.599*10^8 m/s



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