In the previous log, we showed the spectrum generated by a white LED passed through a diffraction grating. While it demonstrated the principle of diffraction, the individual diffraction orders weren't clearly visible. This time, we've built a simple tabletop setup to show these orders distinctly using two lasers.

The Experimental Setup

To get a clear visual of the different orders, we used a red and a blue laser. These beams are combined using a beam combiner and then directed at a diffraction grating. The grating splits the light into various paths, which we then observe on a screen.

Here is an image of our setup, showing all the components.

Understanding Diffraction Orders

When light hits a diffraction grating, it is reflected or transmitted at specific angles, creating a pattern of bright spots called diffraction orders.

1. The zero-order mode (n=0) is the direct reflection or transmission, traveling in the same direction as the incident light. It's often the brightest spot.
2. The +1 order (n=+1) is found on the same side as the angle of incidence.
3. The -1 order (n=−1) is found on the opposite side of the incident angle.

Based on the incident angle and the grating's properties, you can see many more orders, such as +2, -2, and so on.

When we power on just the red laser, we see the clear zero, +1, and -1 orders on the screen.

 We then turn on the blue laser, and you can see its orders appear in different positions relative to the red laser's orders. This is because the angle of diffraction is dependent on the wavelength of the light.

The Diffraction Grating Equation

The behavior of the diffracted light is governed by the diffraction grating equation. This equation relates the angle of the diffracted orders to the wavelength of the light and the spacing of the grating. The equation for a transmission grating is:

where, 

• d is the spacing between the lines (grooves) on the grating.
• θm is the angle of the m-th diffraction order.
• m is the diffraction order (an integer: 0, ±1, ±2, ...).
• λ is the wavelength of the incident light.

This equation shows why the red and blue lasers produce diffraction orders at different angles. Since the red laser has a longer wavelength (λ) than the blue laser, its diffraction orders appear at larger angles for the same grating (d).

In our next log, we'll discuss what happens when these orders overlap and the issues that can arise from it.