the formula to calculate reflectivity like bragg mirror model and fresnel consider refractive index of a material in order to define the reflectivity. but it does not state whether the curvature of the lens, in this case convex affect the reading of reflectivity or not. mostly I found the formula is used for a flat/planar surface. so, how to calculate reflectivity of a surface such as convex lens?
Well the full Fresnel equations include angle of incidence and polarization.
First, variability of reflectance with respect to incidence angle is usually ignored in optics - because it is both small, and its variability is also small near normal incidence. If you are using ordinary spherical lenses, you can probably assume the paraxial approximation, meaning beam angles are small. So - reflectivity is a small quantity to begin with, beam incidence is always very close to normal, where changes in reflectivity are small. Therefore the overall effect is not great.
Second, optics frequently have coatings on them. Accounting for angular dependce of reflectivity of these coatings is difficult (especially not knowing their precise structure). However, these coatings are usually designed for wide angles and again - the paraxial approximation allows these changes to be ignored.
Third, if we are indeed interested in very small imperfections, then you can imagine that a lens acts as a spatially-varying attenuator. Which will introduce aberrations into the beam. However, the scale of these aberrations is extremely small. Primary aberrations such as spherical, coma, and astigmatism are likely to be far greater problems.
https://en.wikipedia.org/wiki/Fresnel_equations
If you think about a ray tracing model then for most optical systems the angles will be small. When the angle is small cos(x) ~1 and sin (x) is ~0. For angles less than about 20 degrees then the reflectivity will be about the same as if the light was normal. since for many optical systems where lens are used for imaging the angles are kept small it is o.k. to approximate using the normal incident value.
https://en.wikipedia.org/wiki/Fresnel_equations#/media/File:Fresnel_reflection.svg
If for some reason you need to have the total amount of reflected light, You can integrate the reflection using the fresnel equation for each polarization over the area of the lens. This would be tedious and the usually not worth the effort,
- Badges
- Science topic
- Similar topics
- Psychology
- Mental Processes
- Learning