Answer:
a
The the speed of light in the gemstone is [tex]v= 0.599*10^8 m/s[/tex]
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 [tex]i = 80^o[/tex]
The angle of refraction [tex]r = 15.2^o[/tex]
From Snell's law we have ,
[tex]n_1 sin \theta_1 = n_2 sin \theta_2[/tex]
Where [tex]n_1[/tex] is the refractive index of the first medium (water) with a constant value of [tex]n_1 = 1..333[/tex]
[tex]n_2[/tex] is the refractive index of the second medium (gem stone)
[tex]\theta_1[/tex] is the angle between the beam and perpendicular surface of the first medium
[tex]\theta_2[/tex] is the angle between the beam an the perpendicular surface of the second medium
Making the [tex]n_2[/tex] the subject of the formula
[tex]n_2 = n_1 \frac{sin \theta_1}{sin \theta_2}[/tex]
[tex]= (1.333)(\frac{sin (80.0)}{sin 15.2} )[/tex]
[tex]= 5.007[/tex]
Generally refractive index of a material is mathematically represented
[tex]n = \frac{c}{v}[/tex]
Where c is the speed light
v is the speed of light observed in a medium
Making v the subject
[tex]v = \frac{c}{n}[/tex]
substituting value for gem stone
[tex]v = \frac{3.0*10^8}{5.007}[/tex]
[tex]v= 0.599*10^8 m/s[/tex]
