A sapphire is placed in water. An incoming beam of light inside the water hits the sapphire at 35 degrees. What angle will the light ray refract at? SHOW YOUR WORK!
The angle of refraction (θ2) can be calculated using Snell's Law:
n1sinθ1 = n2sinθ2
where n1 is the refractive index of the medium the light is entering (in this case, water) and n2 is the refractive index of the medium the light is leaving (in this case, sapphire).
The refractive index of water is 1.33 and the refractive index of sapphire is 1.77.
Therefore,
1.33sin35 = 1.77sinθ2
sinθ2 = (1.33sin35)/1.77
θ2 = arcsin((1.33sin35)/1.77)
θ2 = 22.2 degrees
To find the angle at which the light ray will refract, we can use Snell's law, which relates the angle of incidence and angle of refraction to the indices of refraction of the two mediums.
Snell's law states: n1 * sin(theta1) = n2 * sin(theta2)
Where:
- n1 is the index of refraction of the first medium (in this case, water)
- n2 is the index of refraction of the second medium (in this case, sapphire)
- theta1 is the angle of incidence of the light ray in the first medium (inside the water)
- theta2 is the angle of refraction of the light ray in the second medium (inside the sapphire)
To find theta2, we need to find the indices of refraction of water and sapphire. The refractive index of water is around 1.33, and the refractive index of sapphire is around 1.77.
Now let's solve for theta2:
n1 * sin(theta1) = n2 * sin(theta2)
1.33 * sin(35) = 1.77 * sin(theta2)
sin(theta2) = (1.33 * sin(35)) / 1.77
Now, we can take the inverse sine of both sides to find theta2:
theta2 = arcsin((1.33 * sin(35)) / 1.77)
Using a calculator, we find that theta2 is approximately 25.3 degrees.
Therefore, the light ray will refract at an angle of approximately 25.3 degrees inside the sapphire.
To find the angle at which the light ray refracts when it passes through the sapphire, we can use Snell's law. Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of light in the two mediums.
The equation for Snell's law is: n1 * sin(theta1) = n2 * sin(theta2)
Where:
n1: refractive index of the medium from which the light is coming (water)
n2: refractive index of the medium the light is entering (sapphire)
theta1: angle of incidence (inside the water)
theta2: angle of refraction (inside the sapphire)
We need to know the refractive indices of water and sapphire to solve the problem. The refractive index of water is approximately 1.33 and the refractive index of sapphire is around 1.77.
Given that the angle of incidence inside the water is 35 degrees, we can plug the values into Snell's law to find the angle of refraction inside the sapphire.
1.33 * sin(35) = 1.77 * sin(theta2)
Now, let's solve for theta2:
sin(theta2) = (1.33 * sin(35)) / 1.77
Using a scientific calculator or trigonometric tables, we can find the value of sin(theta2).
Finally, we need to take the inverse sine (sin^-1) of that value to find theta2, the angle of refraction.
theta2 = sin^-1[(1.33 * sin(35)) / 1.77]
The resulting value will be the angle at which the light ray refracts inside the sapphire.