Question

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?

Answers

  1. Answer:

    a

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

    b

    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

    c

    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

    Explanation:

      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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