• Pays/Région
  • Bonjour Mon compte
  •   
 

 
Beam Displacement Calculator

View All Technical Tools

Angle of Incidence, θ (degrees):

Thickness of Plate, t (mm):

Refractive Index of Medium, n:

Beam Displacement, s (mm) : --     

Displacement of Secondary Reflection, x (mm): --     

Focal Length Calculator
$$ s = t \cdot \sin{\theta} \left( 1 - \frac{\cos{\theta}}{\sqrt{n^2 - \sin^2{\theta}}} \right) $$
$$ x = \frac{t \cdot \sin{\left( 2 \theta \right)}}{\sqrt{n^2 - \sin^2{\theta}}} $$
s Beam Displacement
x Displacement of secondary reflection
θ Angle of incidence between beam and plate normal
t Thickness of plate
n Refractive index of medium

Note: This calculator is valid within the following limits: t > 0mm, 0° < θ < 90°, n > 0

Description

Determine the displacement of a collimated beam incident on a tilted plane-parallel plate, or window. This displacement is dependent on the angle of incidence, the thickness of the plate, and the refractive index of the plate. This calculator also determines the displacement of the secondary reflection resulting from a small portion of the beam reflecting off the glass-air interface of the plate.

The exit beam will be parallel to the input beam and magnification remains constant when imaging through a plane-parallel plate.

Example

Question: What is the displacement of a beam and its secondary reflection when the beam passes through a 10mm thick N-BK7 plate at an angle of incidence of 15 degrees?

Answer: The beam displacement and secondary reflection displacement can be determined by:

$$ s = \left( 10 \text{mm} \right) \sin{\left( 15° \right)} \left( 1 - \frac{\cos{\left( 15° \right)}}{\sqrt{1.517^2 - \sin^2{\left(15° \right)}}} \right) = 0.916 \text{mm} $$
$$ x = \frac{\left( 10 \text{mm} \right) \sin{\left( 2 \cdot 15° \right)}}{\sqrt{1.517^2 - \sin^2{\left( 15° \right)}}} = 3.499 \text{mm} $$

The displacement of the beam is 0.916mm and the displacement of the beam’s secondary reflection is 3.499mm.

Related Resources

 Application Note

Related Product Category: Optical Windows

View All Now

Besoin d'une offre ? Insérez un numéro de stock pour recevoir votre devis !

Edmund Optics Facebook Edmund Optics Twitter Edmund Optics YouTube Edmund Optics LinkedIn Edmund Optics Instagram



EO EST MEMBRE DE :

Spectaris Optence Photonics21 Epic EMVA EOS Photonics France

×