Chapter 18Refraction & lensesMr. Barry Latham, M.A.EdHonors PhysicsBloom High School

18.1 Snell’s Law Stinks!• Light travelling through a substance depends on the density of

the material• Density leads to an ‘index of refraction,” n (unitless ratio) • n is independent of the q1, it only depends on the material

• n1sin(q1)=n2sin(q2)• Because they are equal, it doesn’t matter if q1=qi and q2=(the other one)• Correspond n1 to q1 and n2 to q2!

Material n

Air 1.0003Water 1.33

Glycerin 1.47Immersion Oil 1.515

Glass 1.52Flint 1.66

Zircon 1.92Diamond 2.42

Lead Sulfide 3.91

Solving for n• Prac Prob 5• A block of unknown material is submerged in

water. Light in the water is incident on the block at an angle of 31°. The angle of refraction of the light in the block is 27°. What is the index of refraction of the material of the block?

• n1sin(q1)=n2sin(q2)• (1.33)(sin 31)=(n2)(sin 27)

• Solving for n• (1.33)(sin 31)/(sin 27)=n2

• 1.50 (crown glass? Immersion oil?)

Solving for q• Prac Prob 1• A laser beam in air is incident upon EtOH at an

angle of 37.0°. What is the angle of refraction?

• n1sin(q1)=n2sin(q2)• (n1)/(n2)sin(q1)=sin(q2)• sin-1((n1)/(n2)sin(q1))=q2

• sin-1((1.0003)/(1.36)sin(37.0))=q2• q2=26.3°

Relationship to c• Particle Model of Light• Photons are absorbed then re-emitted• More particle ‘in the way’ means more absorptions and re-

emissions, which slows the process down• c>v if not in a vacuum• n is an indicator of this process

• n=c/v

Total Internal Reflection• In lieu of refraction, the light will trace the media

boundary• Beyond this angle, the light will reflect• This is the critical angle, qc

• qc is based on the media, so the relationship involves ‘n’• sin qc=n2/n1

• PhET “Bending Light”

Fiber Optics• Total Internal Reflection gone MAD

Mirages• Light is bent as it passes through two different

media• Cooler air (n is large) and Warmer air (n is smaller)

18.2 Convex & Concave Lenses• Convex- thicker in the middle• Concave- thinner in the middle

• Thin Lens Equation• 1/f=1/di+1/do

• f=focal length• di=distance from lens to image• do=distance from lens to object• Units don’t matter, as long as they’re the same

Magnification• Magnification Equation• m=hi/ho=-di/do

• m=magnification factor• Negative m is a smaller image• Positive m is a larger image

• hi=height of image• ho=height of object

Ray Diagrams• Convex lens (object past f)• Ray 1- from a point on the object parallel to the axis of

symmetry to the plane of the lens, then through the opposite focal point• Ray 2- from the same point of the object through the near

focal point to the plane of the lens, then parallel to the axis of symmetry forward• Ray 3- from the same point of the object straight through

the center of the lens at the axis of symmetry• PhET “Geometric Optics”

Ray Diagrams• Convex lens (object between f and lens)• Ray 1- from a point on the object to the center of the lens

parallel to the axis of symmetry, the through the opposite focal point• Ray 2- from the same point of the object through the near

focal point, then extend the line backwards to the plane of the lens, then backwards and parallel to the axis of symmetry• (not shown here)

• Ray 3- from the same point of the object through the plane of the lens at the axis of symmetry, then backwards

Ray Diagram• Concave lens• Ray 1- from a point on the object parallel to the axis of

symmetry to the center of the lens, then backwards through the near focal point• Labeled B here

• Ray 2- from the same point of the object through the opposite focal point, then extend the line backwards from the plane of the lens parallel to the axis of symmetry• Labeled C here

• Ray 3- from the same point of the object straight through the center of the lens at the axis of symmetry• Labeled A here