What is the critical angle (in degrees) for a ray of light coming from a medium with an index of refraction of 1.4 to a medium with an index of refraction of 1.2? label the unit.
To find the critical angle, you can use the formula:
Critical angle = arcsin(n2 / n1)
Where:
- n1 is the refractive index of the initial medium (1.4 in this case)
- n2 is the refractive index of the final medium (1.2 in this case)
- arcsin is the inverse sine function
Substituting the given values into the formula:
Critical angle = arcsin(1.2 / 1.4)
Using a scientific calculator, you can evaluate the arcsin function to find the critical angle.
The critical angle is approximately 55.94 degrees (rounded to two decimal places).
To find the critical angle, we need to use Snell's law, which relates the angle of incidence and the angle of refraction of a ray of light passing from one medium to another.
Snell's law states:
n1 * sin(θ1) = n2 * sin(θ2)
Where:
- n1 is the index of refraction of the medium the light is coming from (1.4 in this case)
- θ1 is the angle of incidence of the incoming light ray
- n2 is the index of refraction of the medium the light is entering (1.2 in this case)
- θ2 is the angle of refraction of the transmitted light ray
In this case, we want to find the critical angle, which is the angle of incidence that leads to an angle of refraction of 90 degrees (or π/2 radians) when going from a higher refractive index medium to a lower refractive index medium.
Therefore, we can rearrange Snell's law as:
sin(θ1) = (n2 / n1) * sin(θ2)
Since θ2 is 90 degrees, sin(θ2) = 1.
sin(θ1) = (n2 / n1) * 1
sin(θ1) = (1.2 / 1.4)
Now, to find θ1, we need to take the inverse sine (also known as arcsine) of both sides of the equation. The arcsine function gives us the angle whose sine equals the given value.
θ1 = arcsin((1.2 / 1.4))
Using a scientific calculator or a built-in function, you can find the arcsine value of (1.2 / 1.4) and convert it to degrees to get the critical angle.
Note: Make sure your calculator is in degree mode if you want the answer in degrees.