Diffraction

Introduction to Diffraction

• Diffraction is the phenomenon where waves spread out as they pass through an opening or around an obstacle. It is a fundamental property of wave behavior.
• Diffraction is most noticeable when the size of the opening or obstacle is comparable to the wavelength of the wave.

KEY TAKEAWAY: Diffraction demonstrates the wave nature of light and sound, causing them to bend and spread around obstacles.

Factors Affecting Diffraction

Wavelength (\(\lambda\)) and Gap Width (\(w\))

• The extent of diffraction depends on the ratio of the wavelength (\(\lambda\)) of the wave to the gap width (\(w\)) or the size of the obstacle.
• The ratio \(\frac{\lambda}{w}\) is critical in determining the amount of diffraction.

Qualitative Effects of Changing \(\frac{\lambda}{w}\)

• Limited Diffraction: When \(\frac{\lambda}{w} \ll 1\) (wavelength is much smaller than the gap width), diffraction is minimal. The wave passes through the opening with little spreading.
• Significant Diffraction: When \(\frac{\lambda}{w} \gtrsim 1\) (wavelength is comparable to or larger than the gap width), diffraction is significant. The wave spreads out considerably after passing through the opening.
• Increased Diffraction: As the ratio \(\frac{\lambda}{w}\) increases, the extent of diffraction also increases. This means waves with longer wavelengths or passing through smaller openings will diffract more.

EXAM TIP: Pay close attention to the relationship between wavelength and gap size when describing diffraction. A larger ratio λ/w means greater diffraction.

Visual Representation

Imagine water waves approaching a barrier with a small opening:

• Small Opening (Significant Diffraction): If the opening is small compared to the wavelength of the water waves, the waves will spread out in a semi-circular pattern on the other side.
• Large Opening (Limited Diffraction): If the opening is large compared to the wavelength, the waves will pass through with minimal bending, maintaining a more linear wavefront.

Sound Wave Diffraction

• Lower frequency sound waves have longer wavelengths and thus diffract more easily around obstacles compared to higher frequency sound waves. This is why you can often hear someone speaking even when they are around a corner.

APPLICATION: The ability of low-frequency sounds to diffract more easily explains why bass frequencies travel further and are heard more clearly around obstacles.

Diffraction and Imaging

Limitations in Imaging

• Diffraction limits the resolution of imaging devices such as microscopes and telescopes.
• The ability to distinguish between two closely spaced objects is limited by the diffraction of the waves used for imaging (typically electromagnetic waves).

Rayleigh Criterion

• The Rayleigh criterion states that two objects are just resolvable when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other.

• The minimum angular separation (\(\theta\)) that an imaging system can resolve is given by:

  \[ \theta \approx 1.22 \frac{\lambda}{D} \]

  where:

  • \(\lambda\) is the wavelength of the electromagnetic wave.
  • \(D\) is the diameter of the lens or aperture.

Implications for Microscopes and Telescopes

• Microscopes: The wavelength of visible light limits the resolution of optical microscopes. To see smaller objects, shorter wavelengths (e.g., ultraviolet light or electron beams in electron microscopes) are used.
• Telescopes: The diameter of the telescope’s objective lens or mirror affects its resolving power. Larger telescopes can resolve finer details because they have a larger aperture (\(D\)).

COMMON MISTAKE: Confusing diffraction with refraction. Diffraction is the spreading of waves around obstacles, while refraction is the bending of waves as they pass from one medium to another.

Example: Resolving Power of a Telescope

A telescope with a diameter of 2 meters is used to observe stars at a wavelength of 500 nm. The minimum angular separation that the telescope can resolve is:

This means the telescope can distinguish between two stars that are separated by at least \(3.05 \times 10^{-7}\) radians in the sky.

VCAA FOCUS: Exam questions often involve calculating the ratio λ/w and explaining how it affects the extent of diffraction and the resolution of imaging devices.

Summary Table

STUDY HINT: Practice drawing diagrams showing how waves diffract through different sized openings. This will help you visualize the concept and answer qualitative questions.