Calculator
Example Data Table
| Case | Incident Angle | n1 | n2 | Mode | Key Output |
|---|---|---|---|---|---|
| Air to glass | 45.00° | 1.000 | 1.500 | Unpolarized | Transmitted angle 28.1255°, reflectance 5.0240% |
| Air to glass | 56.31° | 1.000 | 1.500 | p-polarized | Brewster condition, p-reflectance near 0% |
| Glass to air | 50.00° | 1.500 | 1.000 | Unpolarized | Total internal reflection occurs |
Formula Used
Law of reflection: θr = θi
Angle from surface: θsurface = 90° − θi
Snell law: n1 sin θi = n2 sin θt
Critical angle: θc = sin−1(n2 / n1) when n1 > n2
Brewster angle: θB = tan−1(n2 / n1)
s reflectance: Rs = ((n1cosθi − n2cosθt) / (n1cosθi + n2cosθt))2
p reflectance: Rp = ((n1cosθt − n2cosθi) / (n1cosθt + n2cosθi))2
Unpolarized reflectance: R = (Rs + Rp) / 2
Mirror tilt rule: reflected ray rotation = 2 × mirror tilt
How to Use This Calculator
- Enter the incident angle.
- Select whether the angle is measured from the normal or the surface.
- Enter refractive index values for the first and second media.
- Choose unpolarized, s-polarized, or p-polarized light.
- Enter a mirror tilt change if you want ray rotation.
- Choose your preferred decimal precision.
- Press the calculate button.
- Review the results shown above the form.
- Use the CSV button to save data.
- Use the PDF button to print the page as a PDF.
Optical Reflection in Physics
Why reflection matters
Optical reflection describes how light behaves at a boundary. The boundary can be a mirror, lens coating, window, fiber end, or polished crystal surface. Good reflection analysis improves measurement quality. It also helps reduce signal loss in precision optical systems.
Angles and reference lines
The main rule is simple. The angle of reflection equals the angle of incidence. Both angles are measured from the normal. The normal is an imaginary line perpendicular to the surface. Many learners confuse surface angle and normal angle. This calculator converts both forms instantly.
Why refractive index changes results
Reflection strength depends on the refractive indices of the two media. Air to glass behaves differently from glass to air. A larger index contrast usually creates stronger reflection. That matters in sensors, microscopes, telescopes, solar panels, and imaging paths.
Polarization effects
Polarization also changes reflectance. s-polarized light and p-polarized light do not reflect equally. At Brewster angle, p-polarized reflection can drop to nearly zero for an ideal interface. That is useful in glare control, laser cavities, and polarization optics.
Total internal reflection
When light moves from a higher index medium to a lower one, a critical angle may exist. Above that angle, no real transmitted ray remains. The wave reflects completely. This total internal reflection principle is essential in fiber optics and light guides.
Mirror tilt behavior
Mirror alignment is another practical topic. A small mirror tilt causes a doubled change in reflected ray direction. That rule is common in optical benches, scanners, interferometers, and steering systems. The calculator reports that beam rotation directly.
Why this calculator helps
This tool combines geometry and Fresnel physics in one place. It gives reflection angle, transmitted angle, critical angle, Brewster angle, and reflectance values. It also supports unpolarized, s, and p light. That makes it useful for study, design, and fast verification.
FAQs
1. What is the law of reflection?
The law states that the angle of reflection equals the angle of incidence. Both angles are measured from the normal, not from the surface itself.
2. Why does the calculator ask for refractive indices?
Indices determine how much light reflects and transmits at an interface. They also control Brewster angle, critical angle, and the transmitted angle from Snell law.
3. What is the difference between s and p polarization?
s polarization is perpendicular to the plane of incidence. p polarization is parallel to that plane. Their Fresnel reflectance values are usually different.
4. When does total internal reflection happen?
It happens only when light travels from a higher refractive index to a lower one and the incident angle exceeds the critical angle.
5. What is Brewster angle?
Brewster angle is the incident angle where ideal p-polarized reflection becomes zero. It depends on the ratio between the two refractive indices.
6. Why is there an option for angle reference?
Some textbooks use the normal. Many practical users think in surface angle. The calculator accepts either input and converts it correctly.
7. Why does mirror tilt double the reflected ray change?
A mirror tilt rotates the surface normal by the same amount. Reflection is symmetric about that normal, so the outgoing ray rotates by twice the tilt.
8. What do the CSV and PDF buttons save?
The CSV button saves the current result table. The PDF button opens browser printing so the page can be saved as a PDF document.