Product added to cart

Beam Displacement Calculator

Beam Displacement, s (mm) : **-- **

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

$$ s = t \cdot \sin{\theta} \left( 1 - \frac{\cos{\theta}}{\sqrt{n^2 - \sin^2{\theta}}} \right) $$ |

$$ x = \frac{t \cdot \sin{\left( 2 \theta \right)}}{\sqrt{n^2 - \sin^2{\theta}}} $$ |

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

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.

**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.

or view regional numbers

QUOTE TOOL

enter stock numbers to begin

Sign-up Today// industry trends, new products, discounts, and technical contentAbout UsAbout UsTradeshows Regional Offices Careers Meet the Team Press Releases Case Studies Compliance TECHSPEC^{®}Brand PartnershipsCustomer CareShippingReturnsHelp CenterGive FeedbackIndustry ExpertiseAdvanced Diagnostics Imaging Solutions Laser Optics Defense OpticsDiscounts & ProgramsAll Discount Programs Vision Integration Partners Volume Discount ServicesEducational Discount Program Educational Award startUP Discounted Products Edmund Scientific Outreach E-procurement PlatformsCatalogsAll Catalogs Digital Catalogs Catalog PreferencesCopyright 2020, Edmund Optics Inc., 101 East Gloucester Pike, Barrington, NJ 08007-1380 USA

California Consumer Privacy Act (CCPA): Do Not Sell My Information

COVID-19 Update