Wave Diffraction and Propagation

Fundamental Principles of Diffraction

• Definition of Diffraction: Diffraction is the bending of waves around the corners of an obstacle. It also refers to the spreading out of waves as they pass through an aperture or opening.

• Wave Characteristics During Diffraction:

  • The wavelength ($\lambda$) of the wave is not affected by diffraction.

  • The speed ($v$) of the wave remains unaltered throughout the diffraction process.

• Wavelength Definition: The wavelength is defined as the physical distance between consecutive crests or consecutive troughs of a wave.

Demonstration and Observation in a Ripple Tank

• Experimental Setup: Straight waves are generated on the water surface in a ripple tank and directed toward two obstacles placed in their path.

• Condition for Maximum Diffraction (Narrow Opening):

  • When the separation between the obstacles is comparable to, less than, or equal to the wavelength of the waves generated ($\text{gap size} \le \lambda$), the diffraction effect reaches its maximum.

  • After traversing the narrow opening, the waves spread out comprehensively in every direction, transitioning from straight wavefronts into circular waves (illustrated in Figure 12.16 (a)).

• Behavior with Wide Openings:

  • When the obstacle separation is large relative to the wavelength ($\text{gap size} \gg \lambda$), the central portion of the wave passes straight through without disturbance.

  • Only the portions of the wave near the edges bend or diffract around the obstacle boundaries (illustrated in Figure 12.16 (b)).

Relationship Between Wavelength and Diffraction Extent

• General Dependence: The extent to which a wave diffracts is determined by the ratio of its wavelength to the width of the gap or obstacle.

• Shorter Wavelengths:

  • Waves characterized by shorter wavelengths experience less diffraction.

  • If the wavelength is substantially smaller than the gap size, the waves travel essentially straight through the aperture with minimal lateral spreading.

• Longer Wavelengths:

  • Waves characterized by longer wavelengths diffract significantly more.

  • When the wavelength is large relative to the dimension of the gap, the wavefronts undergo substantial spreading upon clearing the opening.

Electromagnetic Waves: Ultraviolet versus Infrared Diffraction

• Comparative Diffraction of Light: Because diffraction depends on wavelength, different regions of the electromagnetic spectrum display varying degrees of diffraction when encountering identical openings (Figure 12.17):

  • Ultraviolet (UV) Light: Has a shorter wavelength, defined as $< 400\,nm$. Consequently, ultraviolet light exhibits a smaller diffraction angle ($\theta_1$) and diffracts less.

  • Infrared (IR) Light: Has a longer wavelength, defined as $> 800\,nm$. Consequently, infrared light exhibits a greater diffraction spread ($\theta_2 > \theta_1$) and diffracts more.

Mini Lab: Wave Bending and Density Differences

• Procedure: A pencil is placed into a container of water, tilted so that it leans to one side.

• Observation: When observed directly through the front surface of the glass, the pencil appears distinctly bent at the water's surface.

• Scientific Principle: Light bends when traveling from one substance into another substance of differing density.