SYE6207 Chap.2 Photon Energy, Absorption and Optical Constants
Photon Energy, Absorption and Optical Constants
Join the wave and photon descriptions
Photon energy, frequency and wavelength are linked by E = hν = hc/λ, so shorter wavelength means higher energy. At an interface, incident intensity is divided among transmission, absorption and reflection.
Within an absorbing medium, Beer-Lambert attenuation makes intensity decay exponentially with depth.
Keep propagation and loss separate
The complex refractive index contains a real part n that controls phase speed and refraction and an imaginary part κ that controls absorption through α = 4πκ/λ.
Normal-incidence reflectance depends on the index contrast, while reflection toward the higher-index medium introduces a phase reversal.
The chapter uses unit checks, back-substitution and physical direction to make every calculation auditable.
Track what remains continuous at an interface
Photon frequency and energy remain unchanged when light enters a stationary material, while phase speed and wavelength decrease according to the real refractive index.
Reflection can occur even when absorption is zero because the wave must satisfy boundary conditions at an index discontinuity. The reflected electric field reverses phase when reflecting toward a higher-index medium, an effect that becomes important when several reflected paths interfere in a film.
Attenuation describes intensity loss with distance inside the material.
The coefficient α has inverse-length units, and 1/α is the distance over which intensity falls to 1/e under the simple exponential model. Because α = 4πκ/λ, the wavelength and length units must match. A computed coefficient is physically meaningful only if the model has assigned reflection and scattering separately; otherwise it is an effective loss that includes mechanisms beyond absorption.
What this chapter covers
- 01
Photon energy and wavelength
- 02
Transmission, absorption and reflection
- 03
Beer-Lambert attenuation
- 04
Real and imaginary refractive index
- 05
Normal-incidence reflectance
- 06
Phase change on reflection
Worked example · free
Track a photon across a transparent interface
- 3Convert energy to vacuum wavelength.
- 3Apply n to speed and wavelength.
- 4Calculate reflectance and interpret.
Key terms
- Photon Energy
- The quantized energy E = hν carried by one photon.
- Absorption Coefficient
- The inverse-length rate governing exponential intensity loss.
- Complex Refractive Index
- The combined optical constant n + iκ describing propagation and absorption.
- Reflectance
- The fraction of incident intensity returned from an interface.
- Penetration Depth
- The distance 1/α at which intensity falls to e⁻¹ of its initial value.
Photon Energy, Absorption and Optical Constants FAQ
Which quantities change when light enters a material?
Frequency and photon energy remain fixed across a stationary interface. Phase speed falls by the real refractive index, and wavelength falls by the same factor. Reflection can occur even when the imaginary index and absorption are zero.
How is the imaginary refractive index used?
Use κ in α = 4πκ/λ with compatible length units. A larger κ at fixed wavelength gives stronger attenuation and a shorter penetration depth. It is not the index used to calculate phase speed.
Why should I back-substitute an attenuation result?
Putting α back into exp(−αx) checks the sign, thickness placement and unit conversion. A passive sample should not produce negative absorption or a predicted transmittance above one under the simple model.
Can a transparent material still reflect light?
Yes. Reflection follows from the refractive-index contrast at an interface and does not require an imaginary index. A material with negligible absorption can still return substantial intensity when its real index differs from its surroundings.
What does penetration depth mean?
Under exponential attenuation, 1/α is the distance at which intensity has fallen to about 37 per cent of its entry value. It is a characteristic sampling scale, not a sharp boundary beyond which no signal exists.
Exam move
Practise one four-line template: energy to vacuum wavelength, index to in-material speed and wavelength, κ to absorption, and index contrast to reflectance. After every result write a direction check. Use metres or nanometres consistently before applying α, because unit mismatch is more common than algebra failure. Add a final back-substitution and interpret 1/α as a sampling scale.
When several channels are present, write the energy budget before applying Beer-Lambert so that reflection or scattering is not silently relabelled as absorption. Create three deliberately wrong answers: reversed wavelength-energy direction, mixed nanometres and metres, and reflection counted as absorption. Diagnose each error from units or physical bounds before recomputing.
Then explain which quantities remain fixed at an interface and why transparent media can still reflect. This makes the checks usable when arithmetic is under time pressure.
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