14.6 Diffraction Gratings

• The slit spacing in a diffraction grating determines the angle at which diffraction peaks occur.


  True
• The diffraction pattern produced by a diffraction grating is used to analyze the wavelength composition of light
• The diffraction angle is influenced by the wavelength of light and slit spacing according to $d \sin \theta =$$m \lambda$.


  True
• The diffraction pattern from a grating is used in spectroscopy to analyze the wavelength composition of light
• The first-order peak for a diffraction grating with 5000 lines per centimeter and 500 nm light occurs at approximately $14.48^\circ$.


  True
• The distance between adjacent slits or grooves in a diffraction grating is called the slit spacing
• The diffraction grating equation predicts the angles at which bright fringes occur in the diffraction pattern.


  True
• The diffraction grating equation predicts the angles at which bright fringes
• Match the variable with its definition:

  $d$ ↔️ Slit spacing

  $\theta$ ↔️ Angle of diffraction

  $m$ ↔️ Order of diffraction

  $\lambda$ ↔️ Wavelength of light
• Diffraction gratings are used to separate light into its component wavelengths through diffraction and interference.

  True
• A diffraction grating creates a diffraction pattern of bright and dark regions
• Arrange the key steps in how a diffraction grating produces a diffraction pattern:

  1️⃣ Light passes through slits or grooves

  2️⃣ Light diffracts

  3️⃣ Light interferes constructively at certain angles

  4️⃣ Bright fringes are created
• The diffraction grating equation $d \sin \theta =$$m \lambda$ determines the angles at which constructive interference occurs.


  True
• The variable $\lambda$ in the diffraction grating equation represents the wavelength of light
• What does the variable $\theta$ represent in the diffraction grating equation?


  Angle of diffraction
• What does the variable $\lambda$ represent in the diffraction grating equation?


  Wavelength of light
• What is the path difference between waves from adjacent slits in a diffraction grating?

  $d \sin \theta$
• What is the diffraction grating equation?

  $d \sin \theta =$$m \lambda$
• What is a diffraction grating?

  An optical device with parallel slits
• What does the number of slits in a diffraction grating affect?

  Sharpness and intensity
• Steps involved in the creation of a diffraction pattern using a diffraction grating

  1️⃣ Light passes through slits or grooves

  2️⃣ Light diffracts

  3️⃣ Light interferes

  4️⃣ Bright and dark regions form
• What is the angle $\theta$ for the first-order peak when a grating has 5000 lines per centimeter and light with a wavelength of 500 nm is used?


  $14.48^\circ$
• Match the property of diffraction gratings with its effect on the diffraction pattern:

  Slit spacing ↔️ Determines diffraction angle

  Number of slits ↔️ Affects sharpness and intensity

  Wavelength ↔️ Influences diffraction angle
• What are the two main components of a diffraction grating?

  Slits and grooves
• Steps in deriving the diffraction grating equation

  1️⃣ Consider path difference between waves

  2️⃣ Set path difference equal to $m \lambda$

  3️⃣ Apply trigonometric principles

  4️⃣ Derive $d \sin \theta =$$m \lambda$
• What is the diffraction grating equation?

  $d \sin \theta =$$m \lambda$
• The diffraction grating equation is derived by considering the geometry of the grating and the path difference between waves from adjacent slits.


  True
• For constructive interference, the path difference must be an integer multiple of the wavelength
• Match the category with its application:

  Spectroscopy ↔️ Analyzing chemical elements in stars

  Optical Communication ↔️ Wavelength division multiplexing

  Optical Displays ↔️ Creating vibrant images on reflective surfaces

  Scientific Instruments ↔️ Identifying isotopes and molecular structures
• The slit or groove spacing in a diffraction grating determines the angle at which diffraction peaks occur.


  True
• What is slit spacing in a diffraction grating?

  Distance between slits
• In an example, a grating with a slit spacing of $2 \times 10^{ - 6} \text{m}$ and light with a wavelength of $5 \times 10^{ - 7} \text{m}$ produces a first-order bright fringe at $\theta \approx 14.48^\circ$.degrees
• Match the component of a diffraction grating with its function:

  Slits ↔️ Cause diffraction of light

  Grooves ↔️ Enable reflection and diffraction

  Spacing ↔️ Determines diffraction angles
• What does the variable $d$ represent in the context of diffraction gratings?


  Slit spacing
• What does the variable $m$ represent in the diffraction grating equation?


  Order of diffraction
• The diffraction grating equation is derived by considering the geometry of the grating and the path difference between waves from adjacent slits.


  True
• For constructive interference in a diffraction grating, the path difference must be an integer multiple of the wavelength.

  True
• What does the diffraction grating equation predict?

  Bright fringe angles
• What equation is used to solve diffraction grating problems?

  $d \sin \theta =$$m \lambda$
• A diffraction grating has 5000 lines per centimeter. What is the wavelength of light that produces a first-order maximum at an angle of 30 degrees?

  $500 \, \text{nm}$