Find the angle of refraction if there is one. If there isn't, tell which substance reflects the light:
n=1.36
~~~~~~~~~~~Angle=15.60 degrees
n=1.73
~~~~~~~~~~~Angle=17.94 degrees
n=1.51
~~~~~~~~~~~Angle=27.71 degrees
n=1.0003
~~~~~~~~~~~Angle=11.08 degrees
n=2.42
~~~~~~~~~~~Angle=13.80 degrees
n=1.95
I solved for all of the angles using Snell's law, but I don't know how to tell if there's no angle of refraction and which substance would reflect the light.
There is no refraction angle (A2) if the sine of the computed angle (using Snell's law) is equal to or greater than 1.
N1 sin A1 = N2 sin A2
sin A2 = (N1/N2) sin A2 < 1
sin A2 < N2/N1;
otherwise there is only total internal reflection
To determine if there is no angle of refraction and which substance reflects the light, we need to understand Snell's law. Snell's law states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the speeds of light in the two media, which is also equal to the ratio of the refractive indices of the two media.
The formula for Snell's law is given as:
n₁sinθ₁ = n₂sinθ₂
Where:
n₁ is the refractive index of the first medium (initial medium)
θ₁ is the angle of incidence in the first medium
n₂ is the refractive index of the second medium (final medium)
θ₂ is the angle of refraction in the second medium
Using this formula, we can find the angle of refraction for each given refractive index.
1. For n=1.36:
Given n₁ = 1 (air)
n₂ = 1.36
θ₁ = 15.60 degrees
To find θ₂, we rearrange Snell's law as:
sinθ₂ = (n₁/n₂)sinθ₁
Plugging in the values, we get:
sinθ₂ = (1/1.36)sin(15.60)
Using a calculator, we can find the value of sinθ₂ as:
sinθ₂ ≈ 0.2035
Now, to find θ₂, we take the inverse sine of the value:
θ₂ ≈ sin⁻¹(0.2035)
θ₂ ≈ 11.73 degrees (approximately)
Therefore, for n=1.36, the angle of refraction is approximately 11.73 degrees.
2. For n=1.73:
Given n₁ = 1 (air)
n₂ = 1.73
θ₁ = 17.94 degrees
Using the same process, we can find θ₂:
sinθ₂ = (1/1.73)sin(17.94)
sinθ₂ ≈ 0.2816
θ₂ ≈ sin⁻¹(0.2816)
θ₂ ≈ 16.10 degrees
Hence, for n=1.73, the angle of refraction is approximately 16.10 degrees.
3. For n=1.51:
Given n₁ = 1 (air)
n₂ = 1.51
θ₁ = 27.71 degrees
Applying Snell's law, we calculate θ₂:
sinθ₂ = (1/1.51)sin(27.71)
sinθ₂ ≈ 0.4995
θ₂ ≈ sin⁻¹(0.4995)
θ₂ ≈ 30.14 degrees
Thus, for n=1.51, the angle of refraction is approximately 30.14 degrees.
4. For n=1.0003:
Given n₁ = 1 (air)
n₂ = 1.0003
θ₁ = 11.08 degrees
Using Snell's law, we obtain θ₂:
sinθ₂ = (1/1.0003)sin(11.08)
sinθ₂ ≈ 0.1995
θ₂ ≈ sin⁻¹(0.1995)
θ₂ ≈ 11.52 degrees
Therefore, for n=1.0003, the angle of refraction is approximately 11.52 degrees.
5. For n=2.42:
Given n₁ = 1 (air)
n₂ = 2.42
θ₁ = 13.80 degrees
Applying Snell's law, we calculate θ₂:
sinθ₂ = (1/2.42)sin(13.80)
sinθ₂ ≈ 0.2425
θ₂ ≈ sin⁻¹(0.2425)
θ₂ ≈ 14.31 degrees
For n=2.42, the angle of refraction is approximately 14.31 degrees.
Finally, for n = 1.95, there is no given angle of incidence. Therefore, we cannot find the angle of refraction using the given information.
However, we can determine if there is total internal reflection or if the light is reflected back into the same medium by comparing the refractive index of the medium (n = 1.95) with that of surrounding media. If the refractive index of the medium is higher than the surrounding media, then there will be total internal reflection. If it is lower, the light will be transmitted into the surrounding medium.
In this case, since we don't have the refractive indices of the surrounding media, we cannot determine whether the light will be reflected or transmitted.
In summary, we were able to find the angles of refraction for all given refractive indices except for n=1.95. Additionally, without the surrounding media's refractive indices, we cannot determine if the light will be reflected or transmitted.