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?

Answer 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

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

              $v= 0.599*10^8 m/s$