14.6 Diffraction Gratings

• Slit/groove spacing in a diffraction grating determines the angle at which diffraction peaks occur

  True
• What does the grating equation relate?

  Diffraction angle, wavelength, grating spacing
• What is the grating equation used to calculate?

  Constructive interference angles
• When light passes through the slits of a diffraction grating, each slit acts as a new source of waves
• Diffraction gratings work by causing diffraction and interference of light waves.
• What is one tool that uses diffraction gratings to analyze light's wavelength composition?

  Spectroscopy
• The angle of diffraction must be in radians when using the grating equation.


  True
• What is one application of diffraction gratings in spectroscopy?

  Wavelength separation
• The variable $m$ in the grating equation is called the order number.
• Steps in the process of light passing through a diffraction grating

  1️⃣ Light waves pass through the grating slits

  2️⃣ Each slit acts as a new source of waves

  3️⃣ Waves interfere constructively and destructively

  4️⃣ A diffraction pattern is formed
• What happens to the waves when they interfere constructively in a diffraction grating?

  Bright fringes appear
• To calculate the wavelength of light using the grating equation, the angle $\theta$ must be in radians if required.


  True
• Match the order number with its description:

  $m =$$0$ ↔️ Central maximum

  $m =$$1$ ↔️ First-order maximum

  $m =$$- 1$ ↔️ Diffraction peak on opposite side
• What does the order number (m) in a diffraction grating's pattern represent?

  Constructive interference peaks
• What do negative values of m denote in diffraction gratings?

  Diffraction peaks on opposite side
• A reflection diffraction grating has a reflective surface with parallel grooves.
• What is the purpose of diffraction gratings in spectrometers?

  To disperse light into a spectrum
• A diffraction grating creates a diffraction pattern of bright and dark regions
• Steps in the process of how a diffraction grating works

  1️⃣ Light waves pass through the slits or grooves of the grating

  2️⃣ Each slit acts as a new source of waves

  3️⃣ The waves spread out in all directions

  4️⃣ The waves interfere with each other

  5️⃣ Constructive interference occurs at certain angles
• The wavelength of light affects the diffraction angles in a diffraction grating


  True
• Match the principle of diffraction gratings with its explanation:

  Diffraction ↔️ Waves spread out from each slit

  Interference ↔️ Waves interfere constructively and destructively

  Grating Equation ↔️ Relates diffraction angle, wavelength, and grating spacing
• Each slit in a diffraction grating acts as a source of waves that spread out due to diffraction.


  True
• Different wavelengths of light are diffracted at different angles by a diffraction grating.
• If light passes through a diffraction grating with a grating spacing of 1.0 \times 10^{ - 6}</latex> meters, the first-order maximum is observed at $30^\circ$. The wavelength of the light is approximately 500 nm.
• A diffraction grating is an optical device with a large number of parallel, equally spaced slits or grooves.
• What does $d$ represent in the grating equation?


  Grating spacing
• In diffraction, each slit acts as a new source of waves.


  True
• When light waves pass through a diffraction grating, each slit acts as a new source of waves that spread out in all directions.
• The grating equation predicts the angles at which bright fringes appear in the diffraction pattern.
• The wavelength of light calculated in the example is 500 nm.
• Diffraction observed at $m =$$1$ is called the first-order maximum.


  True
• Positive values of m refer to first-order, second-order, third-order, and so on, maxima.
• What is the grating equation used to find the order number in diffraction gratings?

  $m =$$\frac{d \sin \theta}{\lambda}$
• Diffraction gratings are used in spectroscopy to analyze the wavelength composition of light
• In a diffraction grating, slit spacing determines the angles of diffraction peaks
• The grating equation relates grating spacing, diffraction angle, order number, and wavelength
• In the grating equation $d \sin \theta =$$m \lambda$, the term $d$ represents the grating spacing.
• The grating equation relates the diffraction angle, wavelength, and grating spacing.

  True
• Steps to calculate wavelength using the diffraction grating equation

  1️⃣ Identify the grating spacing $d$, angle of diffraction $\theta$, and order number $m$

  2️⃣ Rearrange the grating equation to solve for $\lambda$

  3️⃣ Substitute the known values into the equation

  4️⃣ Calculate the value of $\lambda$
• Match the property of a diffraction grating with its description:

  Slit spacing ↔️ Distance between slits, determines diffraction peak angles

  Number of slits ↔️ Affects sharpness and intensity of diffraction pattern

  Wavelength of light ↔️ Determines diffraction angles