Light of wavelength 600 nm passes through a grating with spacing d = 2 \\mu m. At what angle \ heta does the first-order (m=1) maximum occur?

17.5° Using d \\sin \ heta = m\\lambda, \\sin \ heta = (1 \ imes 600 \ imes 10^{-9}) / (2 \ imes 10^{-6}) = 0.3. Therefore \ heta = \\arcsin(0.3) \\approx 17.5°.

If you use a grating with more lines per centimeter (smaller d), what happens to the spacing between the bright spots on the screen?

The spacing increases From d \\sin \ heta = m\\lambda, if d decreases, \\sin \ heta must increase to maintain the same m\\lambda, resulting in a larger diffraction angle and wider spacing on the screen.

Diffraction Grating Spectrum

Visualize diffraction grating spectra with d sin θ = mλ. Adjust wavelength (color-coded), slit spacing, and max order to see angular positions of maxima.

WHAT IS A DIFFRACTION GRATING?

A diffraction grating is an optical component with a periodic structure (thousands of tiny slits) that splits and diffracts light into several beams traveling in different directions. The directions of these beams depend on the spacing of the grating and the wavelength of the light. Because it is highly sensitive to wavelength, gratings are used in spectroscopy to identify the chemical composition of stars and materials.

HOW TO USE THIS VISUALIZATION

1. **Change Wavelength**: Slide the color picker from blue to red. Notice how red light (longer ) diffracts at larger angles than blue light.2. **Adjust Slit Spacing**: Change the distance between lines. Observe that smaller spacing leads to wider separation between diffraction orders.3. **Identify Orders**: Look for the (central maximum), , and peaks on the screen.

CORE FORMULAS

Diffraction Grating Equation

Slit spacing (lines per meter)

Distance to maximum on a screen

AP EXAM CONNECTION

Unit: Unit 6: Geometric and Physical Optics (Topic 6.3)
Learning Objective: LO 6.C.3

COMMON MISCONCEPTIONS

Diffraction only happens with sound (it happens with all waves, including light)
Red light diffracts less than blue light (red has a longer wavelength and diffracts more)

KEY TAKEAWAYS

Diffraction gratings produce much sharper maxima than double slits.
Wavelength determines the angle of diffraction.
The central maximum () is always the color of the source light.
Diffraction provides evidence for the wave nature of light.

PRACTICE QUESTIONS

Q1 (QUANTITATIVE): Light of wavelength 600 nm passes through a grating with spacing . At what angle does the first-order () maximum occur?

Show Answer & Explanation

Answer: 17.5°

Explanation: Using , . Therefore .

Q2 (CONCEPTUAL): If you use a grating with more lines per centimeter (smaller ), what happens to the spacing between the bright spots on the screen?

Show Answer & Explanation

Answer: The spacing increases

Explanation: From , if decreases, must increase to maintain the same , resulting in a larger diffraction angle and wider spacing on the screen.