3.7 Diffraction

• Longer wavelengths experience more diffraction
• The shape of a new wavefront in Huygens' Principle is the tangent to the spherical wavelets
• What is a diffraction pattern?

  Intensity distribution of waves
• In the diffraction formula, $m$ represents the order of the minima


  True
• The width of the central maximum and the spacing between the fringes depend on the wavelength and slit width
• What is the condition for the general $m$th minimum in single-slit diffraction?


  $w \sin \theta =$$m\lambda$
• Match the key concepts with their descriptions:

  Wavefront Division ↔️ The slit is divided into smaller segments

  Path Difference ↔️ The difference in distance traveled by waves

  Destructive Interference ↔️ Minima occur when waves cancel each other
• Longer wavelengths experience more diffraction than shorter wavelengths

  True
• The new wavefront in Huygens' Principle is the tangent to the spherical wavelets
• Shorter wavelengths produce a narrower diffraction pattern
• What is diffraction?

  Bending of waves
• What does Huygens' Principle state?

  Wavelets form new wavefront
• What are the two factors that affect diffraction?

  Wavelength and slit width
• What is the formula for the position of diffraction minima?

  $\sin\theta =$$\frac{m\lambda}{w}$
• What does the diffraction pattern from a single slit consist of?

  Central bright maximum
• The formula for the first minimum in single-slit diffraction is $w \sin \theta =$$\lambda$


  True
• Wavefront division is a key concept in deriving diffraction minima

  True
• Diffraction is the bending of waves around obstacles or through openings
• What does Huygens' Principle state about every point on a wavefront?

  Acts as a source of wavelets
• What is the diffraction pattern?

  Intensity distribution of diffracted wave
• The formula for the first minimum in a single-slit diffraction pattern is $\sin\theta =$$\frac{\lambda}{w}$


  True
• Match the factors with their effects on the diffraction pattern:

  Wavelength ↔️ Shorter wavelengths result in narrower patterns

  Slit Width ↔️ Narrower slits result in wider patterns
• The position of the first minima in the diffraction pattern is given by $\sin\theta =$$\frac{m\lambda}{w}$


  True
• Match the concept with its explanation:

  Wavefront Division ↔️ Slit is divided into smaller segments

  Path Difference ↔️ Difference in distance traveled by waves

  Destructive Interference ↔️ Minima occur when path difference is $m\frac{λ}{2}$
• For the general $m$th minimum, the formula is $w \sin θ_{m} =$$mλ$, where $m =$$1, 2, 3, ...$ is an integer.
• What factors affect the angle of the first diffraction minimum?

  Wavelength and slit width
• What are the characteristics of a diffraction pattern produced by a narrow slit?

  Wider pattern with broad maxima
• What is one real-world example of spectroscopy?

  Chemical analysis of compounds
• What does $\theta$ represent in the single-slit diffraction formula?


  Angle from central maximum
• What effect does shorter wavelength have on a diffraction pattern?

  Narrower diffraction pattern
• What is the central feature of a diffraction pattern?

  Bright central maximum
• For the first minimum, the path difference between waves from the top and bottom halves of the slit must be $\frac{λ}{2}$


  True
• What type of diffraction pattern does a shorter wavelength produce?

  Narrower pattern
• In the formula \sin\theta = \frac{m\lambda}{w}</latex>, $\theta$ represents the angle of the first minimum.
• The diffraction pattern is significantly influenced by the slit width.
• Visible light diffracts as much as radio waves around buildings

  False
• Light passing through a narrow slit bends due to Huygens' Principle


  True
• Shorter wavelengths produce a narrower diffraction pattern.
• What is the path difference between waves from the top and bottom halves of a slit for the first minimum?

  $\frac{\lambda}{2}$
• Steps to derive the formula for diffraction minima

  1️⃣ Divide the slit into two halves

  2️⃣ Consider the path difference between waves

  3️⃣ Set the path difference to $\frac{\lambda}{2}$ for the first minimum

  4️⃣ Express mathematically: $\frac{w}{2} \sin \theta =$$\frac{\lambda}{2}$

  5️⃣ Simplify to: $w \sin \theta =$$\lambda$