Respuesta :
Answers:
1) 1.359, 1.403
2) [tex]2.207(10)^{8}m/s[/tex], [tex]2.138(10)^{8}m/s[/tex]
Explanation:
The described situation is known as Refraction.
Refraction is a phenomenon in which a wave (the light in this case) bends or changes it direction when passing through a medium with a refractive index different from the other medium.
In this context, the Refractive index [tex]n[/tex] is a number that describes how fast light propagates through a medium or material, and is defined as the relation between the speed of light in vacuum ([tex]c=3(10)^{8}m/s[/tex]) and the speed of light [tex]v[/tex] in the second medium:
[tex]n=\frac{c}{v}[/tex] (1)
On the other hand we have the Snell’s Law:
[tex]n_{1}sin(\theta_{1})=n_{2}sin(\theta_{2})[/tex] (2)
Where:
[tex]n_{1}[/tex] is the first medium refractive index . We are told is the air, hence [tex]n_{1}\approx 1[/tex]
[tex]n_{2}[/tex] is the second medium refractive index
[tex]\theta_{1}[/tex] is the angle of the incident ray
[tex]\theta_{2}[/tex] is the angle of the refracted ray
Knowing this, let's begin with the answers:
1) Indexes of refraction for red and violet light
1a) Red light
Using equation (2) according to Snell's Law and [tex]\theta_{1}=57.0\º[/tex] [tex]\theta_{2}=38.1\º[/tex]:
[tex](1)sin(57.0\º)=n_{2}sin(38.1\º)[/tex]
Finding [tex]n_{2}[/tex]:
[tex]n_{2}=\frac{sin(57.0\º)}{sin(38.1\º)}[/tex]
[tex]n_{2}=1.359[/tex] (3)>>>Index of Refraction for red light
1b) Violet light
Again, using equation (2) according to Snell's Law and [tex]\theta_{1}=57.0\º[/tex] [tex]\theta_{2}=36.7\º[/tex]:
[tex](1)sin(57.0\º)=n_{2}sin(36.7\º)[/tex]
Finding [tex]n_{2}[/tex]:
[tex]n_{2}=\frac{sin(57.0\º)}{sin(36.7\º)}[/tex]
[tex]n_{2}=1.403[/tex] (4) >>>Index of Refraction for violet light
2) Speeds of red and violet light
1a) Red light
Here we are going to use equation (1):
[tex]n_{red}=\frac{c}{v_{red}}[/tex]
[tex]v_{red}=\frac{c}{n_{red}}[/tex]
Substituting (3) in this equation:
[tex]v_{red}=\frac{3(10)^{8}m/s}{1.359}[/tex]
[tex]v_{red}=2.207(10)^{8}m/s[/tex] >>>>Speed of red light
1a) Violet light
Using again equation (1):
[tex]n_{violet}=\frac{c}{v_{violet}}[/tex]
[tex]v_{violet}=\frac{c}{n_{violet}}[/tex]
Substituting (4) in this equation:
[tex]v_{violet}=\frac{3(10)^{8}m/s}{1.403}[/tex]
[tex]v_{red}=2.138(10)^{8}m/s[/tex] >>>>Speed of violet light
Index of refraction of this glass for red and violet light is 1.359 and 1.403. The speeds of red and violet light in the glass is 2.207×10⁸ m/s and 2.138×10⁸ m/s.
What is Snell's law?
According to the Snell's law, the ratio of index of reflection of the different material is equal to the ratio of incident sine angle and reflective sine angle. It can be given as,
[tex]\dfrac{n_1}{n_2}=\dfrac{\sin\theta_2}{\sin\theta_1}[/tex]
Here, [tex]n_1[/tex] and [tex]n_2[/tex] is the index and reflective index and [tex]\theta_1[/tex] and [tex]\theta_2[/tex] is the incident and reflected angle.
A beam of light strikes a sheet of glass at an angle of 57.0° with the normal in air.
The red light makes an angle of 38.1 degrees with the normal in the glass, while violet light makes a 36.7-degree angle.
- The index of refraction of this glass for blood-red light-
The index of refraction of air is 1. Thus, by the Snell's law,
[tex]\dfrac{1}{n_2}=\dfrac{\sin38.1}{\sin57.0}\\n_2=1.359[/tex]
- The index of refraction of this glass for violet light-
The index of refraction of air is 1. Thus, by the Snell's law,
[tex]\dfrac{1}{n_2}=\dfrac{\sin36.7}{\sin57.0}\\n_2=1.403[/tex]
- The speeds of red light in the glass-
Speed of a particular light in a medium is the ratio of speed of light in vacuum to the index of refraction of that medium.
The speed of light is 3×10⁸ m/s. Thus the speeds of red light in the glass is,
[tex]v=\dfrac{3\times10^{8}}{1.359}\\v=2.207\times10^{8}\rm\; m/s[/tex]
- The speeds of violet light in the glass-
The speeds of violet light in the glass is,
[tex]v=\dfrac{3\times10^{8}}{1.403}\\v=2.138\times10^{8}\rm\; m/s[/tex]
Hence, the index of refraction of this glass for red and violet light is 1.359 and 1.403. The speeds of red and violet light in the glass is 2.207×10⁸ m/s and 2.138×10⁸ m/s.
Learn more about the Snell's law here;
https://brainly.com/question/10112549
