Things You'll Need:
- Refractive index reference
- Pencil
- Paper
- Calculator
- Microsoft Excel (optional)
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Step 1
The equation to calculate the critical angle is: θ = arcsin (n2/n1), where θ is the critical angle, arcsin is the inverse sine (a trigonometry function), n2 is the refractive index of the less dense substance and n1 is the refractive index of the more dense substance. The greater the refractive index, the greater the density of the substance.
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Step 2
Information required to calculate the critical angle includes the refractive index (n1 and n2) of the 2 substances through which the light ray is traveling. The website listed in Resources allows you to select the group and then specify the substance or material. Once those two sections are completed, the database returns the refractive index of the substance.
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Step 3
To manually calculate the critical angle, please refer to the following example and associated formula.
Example: A ray of light passes through from air into the water at a 27 degree angle. The refractive index for water is: 1.333. The refractive index for air is: 1.000293. What is the critical angle?
Θ = arcsin(n2/n1)
Θ = arcsin (1.000293/1.333)
Θ = arcsin (0.750407352)
Θ = 48.625675
Θ = 48.6 degrees.
In this example, the critical angle (48.6 degrees) is greater than the angle of incidence (27 degrees). This means that the light was refracted and reflected as it passed from the air into the water instead of all of the light being reflected. -
Step 4
To calculate the critical angle with Excel, please refer to the following example and associated formulas that need to be entered into the Excel spreadsheet.
The same example will be used to calculate the critical angle with Excel as it was to calculate it manually.
Example: A ray of light passes through from air into the water at a 27 degree angle. The refractive index for water is: 1.333. The refractive index for air is: 1.000293. What is the critical angle?
In Row 1, label columns A through E as follows: "n2," "n1," "n2/n1," "arcsin n2/n1" and "Radians to Degrees (Critical Angle)."
In row 2 enter the following information in each column; A: "1.000293," B: "1.333", C: "=A2/B2," D: "=ASIN(C2)" and E: "=DEGREES(D2)." The critical angle is found in cell E2, 48.6 degrees. -
Step 5
To understand and use the critical angle, it is important to understand the angle of incidence. Information about the angle of incidence is provided here as a reference tool to allow you to use the information from the critical angle calculation.
The angle of incidence is the angle at which a light ray passes through a surface or boundary. The angle of incidence is measured off an imaginary line that is perpendicular to the surface or boundary through which the light ray passes. The greater the angle of incidence, the more the ray of light is parallel to the surface or boundary.
