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Polarizer Angle & Transmitted Light Intensity

Apply Malus’s law to polarized light intensity, analyzer angle and the principal inverse angle.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

An ideal analyzer at 60° to the incident polarization transmits one quarter of the intensity: 100 W/m² becomes 25 W/m². Crossed axes at 90° transmit zero in the ideal model.

Transmitted intensity = incident polarized intensity × cos²(axis angle)

Worked example

Enter these known values and leave the other values blank.

Incident polarized intensity
100 W/ m²
Angle between polarization and analyzer axis
60 deg
Transmitted intensity
25 W/ m²

Assumptions and limitations

  • Incident intensity is positive. Transmitted intensity can be zero and cannot exceed the incident intensity. Unit selectors describe power per area, such as W/m².
  • The incident light is already linearly polarized and the analyzer is ideal. Unpolarized light first passing through an ideal polarizer loses half its intensity; that separate first-polarizer step is not included.
  • Forward calculation is periodic in angle. The inverse returns the principal angle between 0° and 90°; other orientations can give the same intensity. At 90°, floating-point evaluation can leave an extremely small residual instead of exact zero.
  • With crossed axes and zero transmitted intensity, incident intensity cannot be recovered uniquely. Enter the known incident intensity and angle for that boundary. Real polarizers have finite extinction and absorption.

Common questions

Does 60° transmit half the light?

No. The cosine is one half, but intensity uses its square, so the transmitted fraction is one quarter.

Is this the angle at which the light hits a surface?

No. It is the angle between the light’s polarization direction and the analyzer’s transmission axis.

References

Bookify allows zero transmitted intensity and requires it not to exceed positive incident intensity.

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