Presentation on theme: "Ray Optics, Mirrors, Lenses, Image and Optical Instruments"— Presentation transcript:
1 Ray Optics, Mirrors, Lenses, Image and Optical Instruments Chapter 22, 23Ray Optics, Mirrors, Lenses, Image and Optical Instruments
2 A Brief History of Light 1000 ADIt was proposed that light consisted of tiny particlesNewtonUsed this particle model to explain reflection and refractionHuygens1670Explained many properties of light by proposing light was wave-like
3 A Brief History of Light, cont Young1801Strong support for wave theory by showing interferenceMaxwell1865Electromagnetic waves travel at the speed of light
4 A Brief History of Light, final PlanckEM radiation is quantizedImplies particlesExplained light spectrum emitted by hot objectsEinsteinParticle nature of lightExplained the photoelectric effect
5 in the absence of medium. C = f lC: speed of lightC = 3 x 108 m/sin vacuumEM wave can travelin the absence of medium.In other medium, thespeed of light issmaller than in vacuum.
7 How do we see an object? Detection of light directly emitted by object Detection of light reflected by object (most common)
8 Ray Optics – Using a Ray Approximation Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different mediaThe ray approximation is used to represent beams of lightA ray of light is an imaginary line drawn along the direction of travel of the light beams
9 The Index of Refraction Speed of light c= 3x 108 m/s in vacuum.Speed of light is different (smaller) in other mediaThe index of refraction, n, of a medium can be defined
10 Index of Refraction, cont For a vacuum, n = 1For other media, n > 1n is a unitless ratioNormal air:Water: 1.33Flint glass: 1.66Diamond 2.42
11 Reflection of LightA ray of light, the incident ray, travels in a mediumWhen it encounters a boundary with a second medium, part of the incident ray is reflected back into the first mediumThis means it is directed backward into the first medium
12 Specular ReflectionSpecular reflection is reflection from a smooth surfaceThe reflected rays are parallel to each otherAll reflection in this text is assumed to be specular
13 Diffuse ReflectionDiffuse reflection is reflection from a rough surfaceThe reflected rays travel in a variety of directionsDiffuse reflection makes the road easy to see at night
14 Law of Reflection The normal is a line perpendicular to the surface It is at the point where the incident ray strikes the surfaceThe incident ray makes an angle of θ1 with the normalThe reflected ray makes an angle of θ1’ with the normal
15 Law of Reflection, contThe angle of reflection is equal to the angle of incidenceθ1= θ1’
16 Reflection and Mirrors q1 = q1q11Law of reflectionSpecular ReflectionDiffuse Reflection
17 Image forms at the point where the light rays converge. When we talk about an image, start from an ideal point light source.Every object can be constructed as a collection of point light sources.VIRTUALIMAGE|q|pImage forms at the point where the light rays converge.When real light rays converge Real ImageWhen imaginary extension of L.R. converge Virtual ImageOnly real image can be viewed on screen placed at the spot.
18 For plane mirror: p = |q| IMAGEVIRTUALFor plane mirror: p = |q|How about left-right? Let’s check?p: object distanceq: image distance
19 Parallel light rays: your point light source is very far away. Spherical MirrorR: radius of curvaturefocal Pointf: focal length = R/2Optical axisconcaveconvexParallel light rays: your point light source is very far away.Focal point:(i) Parallel incident rays converge after reflection(ii) image of a far away point light source forms(iii) On the optical axis
20 Spherical Aberration Reflected rays do not converge: Not well-defined focal pointnot clear imageSpherical Aberrationf = R/2 holds strictly for a verynarrow beam.Parabolic mirror can fix this problem.
26 For a small object, f = R/2 (spherical mirror) Mirror Equation1/p + 1/q = 1/fFor a small object, f = R/2 (spherical mirror)1/p + 1/q = 2/RAlert!!Be careful with the sign!!Negative means that it is inside the mirror!!p can never be negative (why?)negative q means the image is formed inside the mirrorVIRTUALHow about f?
27 Focal point inside the mirror For a concave mirror: f > 0Focal point inside the mirrorf < 01/p + 1/q = 1/f < 0 : q should be negative.
28 All images formed by a convex mirror are VIRTUAL. 1/p + 1/q = 1/f < 0 : q should be negative.All images formed by a convex mirror are VIRTUAL.Magnification, M = -q/pNegative M means that the image is upside-down.For real images, q > 0 and M < 0 (upside-down).
29 Example: An object is 25 cm in front of a concave spherical mirror of radius 80 cm. Determine the position andcharacteristics of the image.1/p + 1/q = 1/f f = R/2 = 40 cmObject is at the center: p = 25 cm1/q = 1/40 – 1/25=q = cm < 0 (Virtual Image, 66.7 cm behind mirror)M = -q/p = -(-66.7)/25 = 2.7Erect, 2.7 times the size of the object
30 Example: What kind of spherical mirror must be used, and what must be its radius, in order to give an erect image 1/5 asLarge as an object placed 15 cm in front of it?M = -q/p -q/p=1/5So q = -p/5 = -15/5 = -3 cm1/p + 1/q = 1/f 1/15 - 1/3 = 1/f1/f = (1-5)/15f = -15/4 = cmR = 2 f = -7.5 cm Convex
31 Example: Where should an object be placed with reference to a concave spherical mirror of radius 180 cm in order to form aReal image having half its size?M = -q/p -q/p=-1/2So q = p/2f = R/2 = 90 cm1/p + 1/q = 1/f 1/p + 2/p = 1/f3/p=1/90p = 270 cm
32 Refraction Details, 1Light may refract into a material where its speed is lowerThe angle of refraction is less than the angle of incidenceThe ray bends toward the normal
33 Refraction Details, 2Light may refract into a material where its speed is higherThe angle of refraction is greater than the angle of incidenceThe ray bends away from the normal
34 All three beams (incident, reflected, and refracted) are in one plane. Snell’s LawAll three beams (incident, reflected, and refracted) are in one plane.q1q1q2n > 1n1sinq1 = n2sinq2
37 Total Internal Reflection Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refractionRay 5 shows internal reflection
38 Critical AngleA particular angle of incidence will result in an angle of refraction of 90°This angle of incidence is called the critical angle
39 Critical Angle, contFor angles of incidence greater than the critical angle, the beam is entirely reflected at the boundaryThis ray obeys the Law of Reflection at the boundaryTotal internal reflection occurs only when light attempts to move from a medium of higher index of refraction to a medium of lower index of refraction
40 Examples of critical angles (relative to vacuum) SubstanceNCritical angleVacuum190.0Air88.6Ice1.3149.8Water1.33348.6Ethyl Alcohol1.3647.3Glycerine1.47342.8Crown glass1.5241.1Sodium chloride1.5440.5Quartz1.54440.4Heavy flint glass1.6537.3Tooth enamel1.65537.2Sapphire1.7734.4Heaviest flint glass1.8931.9Diamond2.4224.4
41 qf = 2qc Fish vision qc = sin-1(1/1.33) = 49 How could fish survive from spear fishing?Fish visionqf = 2qcqc = sin-1(1/1.33)= 49
45 Thin LensesA thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a planeLenses are commonly used to form images by refraction in optical instruments
46 Thin Lens Shapes These are examples of converging lenses They have positive focal lengthsThey are thickest in the middle
47 More Thin Lens Shapes These are examples of diverging lenses They have negative focal lengthsThey are thickest at the edges
49 Same shape lenses: the higher n, the shorter f The focal length of a lens is determined by the shapeand material of the lens.Same shape lenses: the higher n, the shorter fLenses with same n: the shorter radius of curvature,the shorter fTypical glass, n = 1.52Polycarbonate, n = 1.59 (high index lens)Higher density plastic, n ≈ 1.7 (ultra-high index lens)
50 off the optical axis as a point light source. Rules for ImagesTrace principle rays considering one end of an objectoff the optical axis as a point light source.A ray passing through the focal point runs parallel tothe optical axis after a lens.A ray coming through a lens in parallel to the opticalaxis passes through the focal point.A ray running on the optical axis remains on the opticalaxis.A ray that pass through the geometrical center ofa lens will not be bent.Find a point where the principle rays or their imaginaryextensions converge. That’s where the image of the point source.
51 two focal points: f1 and f2 Parallel rays: image at infinite!!
53 positive negative p q f M 1/p + 1/q = 1/f M = -q/p Lens equation and magnification1/p + 1/q = 1/fM = -q/pThis eq. is exactly the same as the mirror eq.Now let’s think about the sign.positivenegativepreal objectvirtual object(multiple lenses)qreal image(opposite side of object)virtual image(same side of object)ffor converging lensfor diverging lensMerect imageinverted image
54 two focal points: f1 and f2 Parallel beams: image at infinite!! 1/p + 1/q = 1/f1/2f + 1/q = 1/f1/q = 1/2fM = -q/p = -1two focal points: f1 and f21/p + 1/q = 1/f1/f + 1/q = 1/f1/q = 0 q = infiniteParallel beams: image at infinite!!
56 real image (opposite side) positive fExample: A thin converging lens has a focal length of 20 cm.An object is placed 30 cm from the lens. Find the imageDistance, the character of image, and magnification.f = 20, p = 301/q = 1/f – 1/p= 1/20 – 1/30= 1/60q = 60real image (opposite side)M = -q/p= -60/30= -2< 0 inverted
57 Magnifier Consider small object held in front of eye Height y Makes an angle at given distance from the eyeGoal is to make object “appear bigger”: ' > y
58 Rays seen coming from here MagnifierSingle converging lensSimple analysis: put eye right behind lensPut object at focal point and image at infinityAngular size of object is , bigger!Outgoing raysRays seen coming from hereyffImage at Infinity
59 (angular) Magnification One can showf must be in cm
60 ExampleFind angular magnification of lens with f = 5 cm