Reflection and Refraction of Light

1. Reflection and Refractionof Light Amy C. Nau, O.D., F.A.A.O

2. Objectives • Index of Refraction • Laws of Reflection • Laws of Refraction

3. Index of Refraction • Recall that in in media other than a vacuum, waves travel more slowly and their wavelength also decreases v=fl • The ratio of velocity of light in a vacuum divided by velocity in another medium is the INDEX OF REFRACTION (n) • n=velocity in vacuum/velocity in medium = c/vm=3.0x108m/s/vm

4. Index of Refraction • Since c is always the greatest, n is always greater than 1. • It is convention to treat the nair as 1.0 • Vacuum 1 • Air (nonpolluted) 1 • Water 1.33 • PMMA 1.49 • Crown glass 1.523 • Diamond 2.417 • Cornea 1.376 • Zeiss hi-index 1.8

5. Index of Refraction • Clinically, patients ask about “high index” glasses. This means that the lenses are thinner, and more light is bent per unit thickness of glass. • The velocity of light decreases and wavelength also decreases, so the nature of light changes, which can take some adjustment. The aberrations also can increase….

6. Dispersion and Index • We know velocity of light varies with wavelength • The index (n) also varies with wavelength • Depends on the optical material (dispersion curve) • Higher index = more dispersion • Index for shorter wavelength is greater than for longer wavelengths • Index of blue light( 1.6 at 400 nm) is greater than for red (1.47 at 400 nm) So, as wavelength increases, velocity increases and index of refraction decreases.

7. Reflection

8. Some definitions INTERFACE: boundary between two media with different indices Water Air n-=1.33 N=1

9. Regular (specular) reflection • Reflected light leaves the surface in definite beams that follows the laws of reflection. Occurs at smooth surfaces. Think of throwing a ball against a wall, or playing pool

10. Diffuse Reflection Incident light is reflected in all directions and the directions cannot be predicted Occurs at irregular surfaces.

11. Reflection

12. Specular Reflection http://www.glenbrook.k12.il.us/gbssci/phys/Class/refln/u13l1d.html

13. Reflection at Plane Surface N The incident angle determines the final direction of the ball Incident and emergent angles are measured from a perpendicular line (normal) to the surface (interface).

14. Law of Reflection Normal Incident ray Incident angle Reflected angle Reflected ray qi qr Medium 1 (n) interface Medium 2 (n’) Refracted ray The angle of incidence is equal to the angle of reflection qi=qr

15. Problem • Ray incident upon two surfaces that are at right angles. Incident angle is 20 degrees. Calculate the reflected angle at each interface and trace path of rays.

16. The amount of light that is reflected depends on: Color (black absorbs, white reflects) Surface (smooth v rough) Angle of incidence (diffuse reflection only) Refractive index (type of medium) % Reflected = (n’-n/n’+n)2 X 100 Fresnel’s Law of Reflection n’=to left of interface and n= to right of interface…….

17. Problem • How much light is reflected at an air water interface? How about water to glass? %R= {(1.33- 1.0)/1.33+1.0)}2 X 100 Answer 2.01% Hirschberg Reflex %R= {1.523-1.0/1.523+1.0)}2 X 100 Answer 4.2% Glasses, lenses etc. % Reflected = (n’-n/n’+n)2 X 100

18. Refraction of light

19. Interface • The boundary between two media with different indices n n’ n n’ n n’ air water air glass glass water

20. Snell’s Law (of Refraction) nsinq = n’sinq’ n= index of material before refraction n’= index of material after refraction • = incident angle q’= refracted angle Incident angle Optical inferface c n n’ c Surface normal Refracted angle

21. Normal Incidence • If a ray of light is travelling perpendicular to the optical interface. The ray of light will change speed but not direction. change speed not direction

22. Refraction problem • Ray strikes air water interface at 30 degrees. What is the angle of refraction? nsinq = n’sinq’ 1.0 sin 30 = 1.33 sin X Sin X= (1.0)(.5)/1.33 = .3759 X= sin-1(.3759) = 22.08 degrees When light travels from medium of lower index to higher index, it bends toward the Surface normal. When traveling from higher to lower, it bends away from normal.

23. Critical Angle- (n>n’) • For a high-low (water to air ,etc) interface, there is a physical limit of 90 degrees for the refracted angle • The incident angle that yields a refracted angle of 90 degrees= CRITICAL ANGLE qc=sin-1(n’/n)

24. Critical Angle Problem • Find the critical angle at an interface between glass (n=1.50) and air qc=sin-1(n’/n) = sin -1 (1.0/1.5) = .667 = sin-1(.667) = 41.80

25. Critical Angle and Total Internal Reflection N • Some general rules: • When light travels from low index to hi index interface, refracted ray bends towards the normal and refracted angle is smaller than incident angle • When light travels from hi to low, ray bends away from normal and the refracted angle is greater than incident angle air n n’ water cornea n n’ air

26. Total Internal Reflection • If incident angle is larger than the critical angle, it is “undefined” and therefracted rayis reflected back into the same medium at the same angle. glass air Used to design reflecting prisms in low vision telescopes, and to calculate n of unknown materials

27. Why can’t we visualize the TM? • The incident angle of the slit lamp beam is larger than the critical angle and the light is reflected back at you. The cornea air interface (high n to low n) causes TIR The gonio lens has a higher n than the cornea, so total internal reflection cannot occur. (eliminates air surface at the cornea) TIR cannot occur when light travels from lower to higher index,so light enters the contact lens and is reflected from the mirror.

28. Refraction through parallel sided elements n3 n2 n1 Internal angles Emergent angle Incident angle Opposite internal angles are equal If n1=n3 then incident angle= emergent angle

29. Use Snell’s law repeatedly to figure out all angles Refraction through parallel sided elements 1.0sin25=1.5sin?=16.3 1.5sin 16.3=1.33sin?=18.45 1.33sin 18.45=1.5sin?=16.3 1.5sin16.3=1.0sin? = 25!! air air 1.33 n3 n2 n4 n1 n5 1.5 1.5 25

30. The perpendicular distance between an incident and emerging ray after traveling through parallel sided elements Lateral displacement air d This can affect the apparent Position of objects…….. air Glass plate n=1.50

31. Why do my feet look weird in the swimming pool…… • When an object in one medium is viewed from another medium, the apparent position of the object differs from the actual position because of lateral displacement • The refracted angle is different than the incident angle or vice versa depending on the media n/l=n’/l’

32. Apparent position • Looking from air into water object seems farther

33. Looking from water to air object seems closer

34. Remember • Some general rules: • When light travels from low index to hi index interface, refracted ray bends towards the normal and refracted angle is smaller than incident angle • When light travels from hi to low, ray bends away from normal and the refracted angle is greater than incident angle air n n’ water cornea n n’ air

35. Apparent position problems • Use the formula n/l=n’/l’ • Where n= index where real object is located • n’= index from which it is viewed • l= actual distance of object from interface • l’= apparent distance of object from interface (image)

36. problem • A pebble located at the bottom of a fish tank appears to be 22.5cm from the surface. What is the depth of the water? • n/l=n’/l’ so 1.33/l=1.0/22.5 and • l=(1.33)(22.5)= 30 cm

37. The time for light to travel a distance (d) in a medium with an index (n) is expressed by: t=dmeters/v sec It can also be expressed in terms of index ( where n=c/v) t=nd/c =(c/v)d/c =cd/cv=d/v The terms nd is optical path length Time to travel is nd/c Fermat’s Principle

38. Fermat’s Principle • Principle of least time - the path traveled by light will be that which requires the least time. n=1.33 n=1.55 n=1.70 10cm 3cm 5cm How much time to travel from first to last interface? Just sum the times from Each interface T=nd/c=1/c(n1d1+n2d2+n3d3)= 9.58x10-10 sec

39. Is it moving and shimmering? Buy a poster!Look at this illusion for a while and it willappear to be shimmering and moving.Also: Follow the outermost groove and watch itchange from a groove to a hump as you go around the wheel.

40. Curved Surfaces Object Space Index before refraction (or reflection) n Real objects Virtual images Image Space Index post refraction or reflection n’ Real images Virtual objects + direction of light Positive measurements Negative measurements

41. Curved Surfaces • Real object- object that emits divergent wavefronts. Radius and vergence are negative, Real objects must be to the left of the interface • Real Image- image formed with convergent wavefronts, which have positive values. Located at the right of the interface and can be formed on a screen

42. Curved Surfaces • Virtual object- when convergent wavefront is obstructed by an obstacle (i.e. refracting surface) the position to which the wavefront is headed is the virtual object position. To the right of the interface • Virtual image- when divergent wavefront leaves a refracting surface, the center of curvature of the wavefront is the virtual image position. Located to the left of the interface

43. Curved Surfaces • Gaussian Imaging Equation: Used to calculate object position, image position and power. • A refracting surface changesn • the vergence of light incident upon it. The amount of change is equal to the power of the surface • L’=L+F • L’=emerging vergence after refract • L= incident vergence • F= power of the surface

44. Curved Refracting Surfaces • Any point on a curved surface reflects light according to Snell’s law. • The shape of the surface will determine the size, position, type and quality of the resulting image • Spheres are used for Rx lenses, contacts, IOL’s, instruments • We will only consider one surface for simplicity

45. Curved Surfaces- some concepts • Spherical surface is defined by the radius, curvature or power • Radius- distance from arc to any point • Curvature- reciprocal of radius • Center of curvature - equidistant form any point on surface • Sag- perpendicular distance from chord to surface • Chord- straight line connecting any two points on any arc

46. Curved Surfaces Center of curvature radius chord sag Contact lens formula for sag depth r=y2/2s+s/2

47. Radius-Power Relationship • F=n’-n/r • Clinically, this is commonly used to convert K readings to radius readings. • This is also the premise of a “lens clock”, which is used to measure lens power • Power is + when wavelength converges and - for diverging wavelengths.

48. Curved Mirrors • F=n’-n holds, but since n’=n for mirrors, the formula can be rewritten as F=-2n/r • A concave mirror has + power and a convex mirror has – power!!

50. Reflection at a Plane Mirror Reflecting surface Incident ray Reflected ray Virtual space Virutal object Virtual image Real space Real object Real image