Optics Formulas Formulas to Remember…
Vergence: U+D=V where U=object rays, D= lens power, V= image rays
Power (F)= n’-n/r : Use this if you are given index of refraction or radius of curvature and need to find dioptric power
1/d_{o} + 1/d_{i}= 1/f : Use this to find the location of an object or an image. You can also use this to find the focal length of a lens. This is the “thin lens formula”, which ignores the thickness of the lens.
F=1/f_{2 }: Use this to find the power if you are given the focal length and vice versa
Linear Magnification: Image size/ Object size = d_{i}/d_{o : }You can use this to find out the magnification of an image or object.
Spectacle Magnification: a quick way to think about how much minification or magnification your glasses are causing: M=2% per diopter of power. Recall that minus lenses will minify and plus lenses magnify.
Simple Magnifier- we have not yet reviewed this but it relates to low vision devices. M=D/4 where D= diopters. This is for a standard reference distance of 1/4meter (25cm working distance). If the distance is nonstandard, just replace ¼ with new distance.
Mag of a telescope- again we have not had this yet BUT….M= power of eyepiece/ power of objective
Angular Magnification: tan0_{2}/tan0_{1 : }I doubt you will get anything with this as you do not have a calculator.
Prentice’s Rule for Prism Power: P=FxD use this to calculate the amount of prism in a pair of spectacles. P= prism diopters F=distance from optical center in cm, D= lens power
Approximate Power Fapprox= F1+F2 : Says that the net power is the sum of the front and back surfaces of a lens
Effective Power Fe=F/(1-dF) : Used for vertex distance
Spherical equivalent: SE= sph + ½ cyl
Refracting power of a spherical surface D=n’-n/r. Where D= power, (n’-n) is the difference in refractive index between air and lens, and r is radius of curvature of the surface. This is how we use K readings to figure out if a cornea is flat or steep, and how we use K readings to arrive at the shape of a contact lens.
Power of a thin lens in fluid: Power in air/Power in fluid= (n_{iol}-n_{air})/(n_{iol}-n_{fluid})
IOL power (SRK formula): Power IOL = A-2.5L-0.9K where A is a constant, L= axial length in mm, K= average K readings in diopters.
Most things will be CONCEPTUAL! Don’t panic about the math.