Light Spectrum: Deviation and the Electromagnetic Spectrum study notes

Syllabus Scope for Light Spectrum and Electromagnetic Radiation

• Optical Phenomena via Prisms: Use of a triangular prism to generate a visible spectrum from white light sources.
• The Electromagnetic (EM) Spectrum: Comprehensive study of the spectrum, including the broad classification of radiations arranged specifically in order of increasing wavelength ($\lambda$).
• Deviation and Dispersion: Analysis of how light deviates through a triangular prism and the dependence of this deviation on color and wavelength ($\lambda$).
• Common Properties: Identification of properties shared by all forms of electromagnetic radiation.
• Infrared and Ultraviolet Radiations: Detailed exploration of the specific properties and practical applications/uses of infrared and ultraviolet light.
• Light Scattering: Study of scattering principles with simple real-world applications, such as explaining the blue color of the sky.

Deviation Produced by a Triangular Prism

• Process of Deviation: When a light ray of a single color (monochromatic light) enters an glass triangular prism (labeled $ABC$), it undergoes refraction at two distinct surfaces.
• First Surface Refraction ($AB$):
  • An incident ray $PQ$ strikes the first surface $AB$ at an angle of incidence $i$.
  • The ray is deviated by an angle $\delta_1$ toward the base $BC$ of the prism.
  • Inside the prism, the light travels along the straight path $QR$.
  • The magnitude of $\delta_1$ depends on the angle of incidence ($i$) and the refractive index ($\mu$) of the glass relative to air.
• Second Surface Refraction ($AC$):
  • The interior ray $QR$ strikes the second surface $AC$.
  • The ray is further deviated by an angle $\delta_2$, again toward the base $BC$.
  • The light emerges from the prism as the emergent ray $RS$.
  • The magnitude of $\delta_2$ depends on the angle of incidence at the second surface (which is influenced by the angle of the prism $A$) and the refractive index of air relative to glass.
• Total Angle of Deviation ($\delta$):
  • The total deviation ($\delta$) is defined as the angle between the direction of the emergent ray $RS$ and the original direction of the incident ray (represented by the line $PL$).
  • Mathematical expression for total deviation: $\delta = \delta_1 + \delta_2$.

Factors Affecting the Total Angle of Deviation

• Angle of Incidence ($i$): The specific angle at which light strikes the first surface of the prism.
• Angle of the Prism ($A$): The geometric angle between the two refracting surfaces of the triangular prism.
• Refractive Index ($\mu$): The material property of the prism. Because the refractive index is a function of the color or wavelength ($\lambda$) of the incident light, the deviation is inherently color-dependent.
• Light Wavelength ($\lambda$): The specific color of the incident light directly determines the refractive index it encounters, thereby altering the total angle of deviation.

Dependence of Deviation on Color and Wavelength

• Speed of Light in Media: While light rays of all different colors travel at the same velocity in air or a vacuum, they travel at different speeds when passing through other media, such as glass.
• Relationship Between Speed and Refractive Index: The variation in speed for different colors within a medium causes each color to have a unique refractive index ($\mu$) for that specific material.
• Angular Variance: Because different colors (wavelengths) encounter different refractive indices, they are refracted (deviated) by different amounts when passing through the same prism, leading to the separation of colors.