Calculating Penetration Depth for TIR of Evanescent Waves at Glass-Air Interface

In summary, to calculate the penetration depth of an evanescent wave undergoing TIR from glass to air with an incident angle of 60 degrees, we must first ensure that the critical angle is less than 60 degrees. The wavelength of the incident light is 5000 angstroms and the amplitude is reduced to 1/e times its original value. Writing down equations and drawing a picture can aid in understanding the relationship between the critical angle, penetration depth, and amplitude of the evanescent wave.
  • #1
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Homework Statement

: Calculate the penetration depth of an evanescent wave undergoing TIR from glass (n = 1.5) to air interface, such that the amplitute is reduced to 1/e times its original value. Wavelength of the incident light is 5000 angstroms and 60 degrees. First make sure that incident angle of 60 degrees produces TIR - the critical angle is less than 60 degrees.[/B]

Homework Equations

The Attempt at a Solution



I proved that the critical angle is less than 60 degrees. How does that relate to penetration depth and the amplitute of the evenescent wave?[/B]
 
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  • #2
Try writing down a few of the equations. Drawing a picture can help also.
 

1. What is the equation for calculating penetration depth for TIR of evanescent waves at a glass-air interface?

The equation for calculating penetration depth for TIR (Total Internal Reflection) of evanescent waves at a glass-air interface is given by d = λ/4π(√(n12sin2θ - n22)), where d is the penetration depth, λ is the wavelength of the incident light, n1 is the refractive index of the glass, n2 is the refractive index of air, and θ is the angle of incidence.

2. How does the refractive index of the glass and air affect the penetration depth?

The refractive index of the glass and air directly affect the penetration depth. A higher refractive index for the glass will result in a shorter penetration depth, while a lower refractive index for air will result in a longer penetration depth. This is because a higher refractive index means the light will travel slower through the medium, resulting in a shorter distance for the evanescent wave to propagate.

3. What is the significance of the penetration depth in TIR of evanescent waves?

The penetration depth is significant because it determines the distance that the evanescent wave can travel before it decays. This is important in applications such as TIRF (Total Internal Reflection Fluorescence) microscopy, where the evanescent wave is used to selectively excite fluorophores near the glass surface.

4. Can the penetration depth be manipulated?

Yes, the penetration depth can be manipulated by changing the angle of incidence or the refractive index of either the glass or air. By increasing the angle of incidence, the penetration depth decreases, and by decreasing the angle of incidence, the penetration depth increases. Similarly, by changing the refractive index of the glass or air, the penetration depth can be adjusted.

5. How does the wavelength of the incident light impact the penetration depth?

The wavelength of the incident light also affects the penetration depth. A shorter wavelength will result in a shorter penetration depth, while a longer wavelength will result in a longer penetration depth. This is due to the relationship between wavelength and refractive index in the equation for calculating penetration depth.

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