1 Ch. 22 – Reflection and Refraction of Light 22.1 The ... - Physics

22.3 Reflection and RefractionREFLECTIONIt has been known for a couple thousandyears that light reflecting off of a smoothshiny object does so following a simplerule: The angle of reflection with respect tothe normal to the surface equals the angleof incidence:" 1! = " 1In those early days, a mirror was referred to as a speculum (you might still hear it calledthis in certain fields), so that we use the term specular reflection for this process. Incontrast, rough surfaces produce diffuse reflection or scattering.(a) specular reflection(b) diffuse reflectionUnless otherwise noted, we will use “reflection” to mean “specular reflection”.Example 22.1 The Double-ReflectedLight RayTwo mirrors make an angle of 120° witheach other. A ray is incident on mirror M 1at an angle of 65° to the normal. Find theangle the ray makes with the normal of M 2after it is reflected by both mirrors.2

REFRACTIONWhen light hits a transparent medium, part of it usually travels into the medium, but witha change in direction.The ray that gets bent and travels through the medium is said to be refracted, and theprocess is called refraction. Note that the incident ray, refracted ray, and reflectedray all lie in the same plane, normal to the surface of the interface of the two media.The change in direction of the refractedrays result from the fact that the speed oflight in a medium depends on the nature ofthe medium. This results in an angle ofrefraction that is related to the angle ofincidence:sin! 2sin! 1= v 2v 1= const.This will be then first form of the relationcalled Snell’s Law, after the person whodiscovered it.3

For v 2< v 1! " 2< " 1( case a) For v 2> v 1! " 2> " 1case b( )The light gets bent toward the normal when slowing down, and away from the normalwhen speeding up.Note: these light paths are reversible! They are equally valid with the rays pointing theother way.22.4 The Law of Refractionspeed of light in vacuumIndex of Refraction n !speed of light in medium = c vWhen light passes from one medium into another the frequency f remains constant (orelse waves would have to be selectively created or destroyed). So if v changes and f isconstant, then ! must also change, since v = f ! .Finally:! 1! 2= v 1v 2=cn1cn2= n 2n 1sin! 2sin! 1= v 2v 1= n 1n 2" n 1sin! 1= n 2sin! 2This will be the form of Snell’s Law of Refraction that we will usually use.4

The index or refraction varies from material to material, It will also depend on thewavelength of the light itself:Example: Problem #15A beam of light, traveling in air, strikes the surface of mineral oil at an angle of 23.1°with the normal to the surface. If the light travels at 2.17 x 10 8 m/s through the oil, whatis the angle of refraction?Example: Quick Quiz 3A material has an index of refraction that increases continuously from top to bottom. Ofthe three paths shown, which path will the light ray follow as it passes through thematerial?5

22.5 Dispersion and PrismsThe index of refraction n depends on thewavelength ! of the light. Usually (but notalways) n increases as ! decreases. Thisprocess is called dispersion. (Actually thisis normal dispersion – in those cases wheren increases as ! increases we haveanomalous dispersion).So when light composed of more than a single wavelength crosses from one medium intoanother, different wavelengths get bent by different amounts, and the differentwavelength get separated or dispersed from one another.When light passes through a prism, the angle of deviation " is different for the differentwavelengths. This property can be put to use in the form of a prism spectrometer:Every element has its own “fingerprint” inthe wavelengths of light it emits or absorbs.This can be used to analyze thecomposition of atoms & molecules in thelab, the field, or across the universe.6