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Scientific research calculator | Calculation of diffraction angle and Littrow angle of grating

March 17, 2026 Shopify API WaveQuanta Technical Resources

Scientific Research Calculator | Calculation of Grating Diffraction Angle and Littrow Angle

Introduction

In the field of optics, reflective gratings (Reflective Gratings), as key optical components, are widely used in spectral analysis, laser technology, and optical communication systems. Accurately understanding the

working principle of reflection gratings and its core parameters, such as diffraction angle and Littrow angle, is of great significance for optimizing optical design and improving system performance. This article

aims to systematically explain the basic concepts, related calculation formulas and practical applications of reflection gratings, and illustrate its calculation methods through specific examples.

Concept:

Reflection grating is an optical element with a periodic structure on its surface. When light is incident on the grating surface at a certain angle, the incident light will be diffracted due to the microstructure of the grating, generating diffracted light in multiple directions. The distribution and intensity of diffracted light depend on the parameters of the grating and the properties of the incident light.

The diffraction angle refers to the deflection angle of the diffracted light relative to the incident light. Under a specific diffraction order (Order, m), the angle θm of the diffracted light can be calculated through the grating equation.

The Littrow angle is a diffraction angle in a special case. At this time, the incident light and the diffracted light are in the same plane and in opposite directions, that is, the diffraction angle is equal to the incident angle. The existence of the Littrow angle maximizes the diffraction efficiency of the grating at this angle

, so it has important application value in high-precision spectral analysis.

Calculation formula:

The calculation of the diffraction angle and Littrow angle of the reflection grating is based on the following formula:

1. Diffraction angle formula: where:

N is the light density of the grating, and the unit is usually the number of lines per millimeter (1/mm).
m is the diffraction order, which can be a positive or negative integer.
λ is the wavelength of incident light, in nanometers (nm).
θi is the incident angle in degrees (°).
θm is the diffraction angle in degrees (°). Through this formula, the diffraction angle θ can be solved: θm=arcsin(mλN-sin(θi))

Interactive Calculator: Grating Diffraction & Littrow Angle Calculator

1. Diffraction angle formula:

Where:

N is the light density of the grating, and the unit is usually the number of lines per millimeter (1/mm).
m is the diffraction order, which can be a positive or negative integer.
λ is the wavelength of incident light, in nanometers (nm).
θi is the incident angle in degrees (°).
θm is the diffraction angle, in degrees (°).

Through this formula, the diffraction angle θ can be solved:

2. Littrow angle formula: This formula is applicable when the incident light and the diffracted light are in opposite directions and located in the same plane, ensuring that the grating has the highest diffraction efficiency at this angle.

θm=arcsin（mλN-sin（θi））

Grating density N=600 lines/mm
Incident angle θi=30°
Diffraction order m=1
Wavelength λ=500nm

2. Unit conversion: N=600 lines/mmx1000=600000 lines/mλ=500nm=500x10-9mθi=30°x (π/180)=0.5236 radians

2. Unit conversion:

N=600 lines/mmx1000=600000 lines/m

θi=30°x（π/180）=0.5236 radians

3. Calculate the diffraction angle θm: θm=arcsin (-0.2) = -11.54°

3. Calculate the diffraction angle θm:

4. Calculate the Littrow angle θ: Diffraction angle θm≈−11.54° Littrow angle θ≈8.63°

λ=500nm=500x10-9m

4. Calculate the Littrow angle θ:

Diffraction angle θm≈−11.54°

Littrow angle θ≈8.63°

θm=arcsin（-0.2）=-11.54°

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A "Supervision Award". If you have anything else you need to add, please feel free to contact us. We are very honored to be able to provide some convenience for your scientific research experience. The road to scientific research is long and difficult.

I wish all experts and scholars smooth scientific research and early results!

Littrow angle θ≈8.63°

If you find any problems or errors while using the calculator, please contact us in time, we will make corrections in time, and to thank you for your trust and supervision, we have specially prepared it for you

I wish all experts and scholars success in their scientific research and early results!