Applied Optics. , Physics Department (Room #36-401) , ,

Transcription

1 Applied Optics Professor, Physics Department (Room #36-401) , , Office Hours Mondays 15:00-16:30, Wednesdays 15:00-16:30 TA (Ph.D. student, Room #36-415) , Grades Midterm Exam 30%, Final Exam 30%, Homework 20%, Attend & Quiz 10% Textbook Introduction to Optics (Wiley, New York, 1986) Homepage

2 Optics Reference :

3 Light is a Ray (Geometrical Optics) A. General Properties of Light Rays B. Reflection and Refraction C. Prisms and Dispersion D. Images Formed by Light Rays Reflected and Refracted at Planar Interfaces E. Images Formed by Light Rays Reflected and Refracted at Curved Interfaces F. Thin Lenses G. Ray Tracing Through More Complex Optical Systems H. Ray Aberrations I. Optical Instruments Viewed by Eye J. Ray Optics Description of a Waveguide Trapping Light by TIR Light is a Wave (Physical Optics) A. Wave Basics B. Interference of Two Waves C. Interference in Thin Films D. Interferometers E. Holography F. Diffraction of Light G. Polarization of Light Course outline Light is a Photon (Quantum Optics) A. Where Does Light Come From? Sources of Light B. The Laser C. How Do You Know Light is There? Detecting Light

4 Geometrical Optics - light is a ray Geometrical optics Ignore wave nature of light. No diffraction. Light travels in straight lines. Rays. Rays subjected to reflection and refraction. Obey laws of reflection and refraction. Light Ray Line in direction of flow of radiant energy

5 Geometrical Optics - light is a ray Light Ray : the path along which light energy is transmitted from one point to another in an optical system. Speed of Light : Speed of light (in vacuum): a fundamental (or a defined ) constant of nature given by c = 299,792,458 meters / second = 186,300 miles / second. Index of Refraction

6 Reflection

7 Plane of incidence Incident & reflected rays + normal in same plane normal Incident ray θ i θ r reflected ray

8 Refraction

9 Refraction Snell s Law

10 Refraction Snell s Law n i sin θ = i n t sinθ t ni nt < 0????

11 Negative Refraction : n < 0 RHM N > 1 LHM N = -1

12 Prism and Dispersion

13 Images Formed by Rays Reflected at Planar Interfaces

14 Images Formed by Rays Refracted at Planar Interfaces

15 Prisms to Alter the Orientation of Images

16 Images Formed by Rays Reflected at Curved Interfaces

17 Images Formed by Rays Refracted at Curved Interfaces

18 Image Formation by a Thin Lens

19 Spherical Lens Lens usually have both sides spherical Or, one side flat and the other spherical. Easier to make. lens R 2 R 1

20 Lensmaker s Formula = ( n 1) s s' R R 1 2 n s S

21 Sign Convention Rays travel from left to right. Object distance, S positive if one left of lens negative if on right of lens Image distance, S positive if one right of lens negative if on left of lens R 1 & R 2 positive if centre on right of lens negative if centre on left of lens

22 Plano-concave R 1 > 0 R 2 < 0 R 1 = R 2 < 0 R 1 > 0 R 2 > 0 Bi-convex Plano-convex Meniscus convex R 1 < 0 R 2 > 0 R 1 = R 2 > 0 R 1 > 0 R 2 > 0

23 Focal Points for Converging Lens Parallel rays made to cross at focal point by lens. Focal point f

24 Focal Length Distance from lens to focal point. Parallel rays means S =, S = f so = + = ( n 1) s s' f R R 1 2 or = ( n 1) f R1 R2 Giving the thin lens equation = s s' f

25 Focal Points for Converging Lens Rays from focal point made parallel by lens. Focal point f

26 Focal Points for Diverging Lens Point from which parallel rays appear to diverge after passing through the lens. Focal point f

27 Focal Points for Diverging Lens Point to which converging rays are directed when lens makes rays parallel. Focal point f

28 Positive and Negative Lenses For a converging lens So, f is positive. Converging lenses called positive lens For a diverging lens So, f is negative. 1 1 > R 0 1 R < R 0 1 R 2 Diverging lenses called negative lens

29 Real and Virtual Images Real image One beyond lens (to right) Rays converge onto it. Can be projected onto a screen S positive Virtual image One behind lens (to left) Rays diverge from it. Cannot be projected onto a screen S negative.

30 Real Image Produced by convex (positive) lens Object beyond focus u v Focus Real Image Object Focus f f

31 Virtual Image Can be by concave (negative) lens Object beyond focus Image reduced u -v Focus Object Virtual Image Focus

32 Real and Virtual Objects Real object One in front of lens (to left) Rays diverge from it. S positive Virtual object One beyond lens (to right) Rays converge towards it. S negative.

33 Numerical Aperture (N.A.) Describes the quality of a lens. Depends on size of the lens or aperture of lens working distance refractive index Given by equation N.A. = nsin α n is refractive index between object and lens α is the half acceptance angle of lens.

34 Some examples of N.A In all cases, lens is in air (n = 1) 5mm 20 mm 5mm 10mm α 2.5 mm α 10mm α 2.5 tan α= = sin α = sin ( tan ( 0.25 )) = sin = N. A. = tan α= = sin α = sin ( tan ( 1.0) ) = sin = N. A. = tan α= = sin α= sin ( tan ( 1.0) ) = sin = N.A. = 0.707

35 Power of Lens Power of lens Inverse of the focal length in meters Measured in dioptres, D. P = 1 f I.e. lens focal length 50 cm has power of 1 =

36 Magnification Magnification, M Ratio of image height to object height. object y o y So M = u Positive when image erect i Negative when image inverted y o v y i image

37 Magnification object B y o S C D A S y i image Two similar triangles ABC and DEC So M y = i = S' y S o E

38 Focal point Focal point

39 Combining Lenses More than one lens Thin lens equation applied in turn. Image of one lens is object of next. object intermediate image Final image

40 Ray Tracing Through Complex Optical Systems

41 Losses and Aberrations of Rays

42 Aberrations Imperfections reduce theoretical resolution of lens. As N.A. increases, aberrations get worse. Increases with increasing lens power Many different types of aberrations. Chromatic Spherical Coma Curvature of field etc.

43 Chromatic Aberration Different colours focused at different points. Combination of lenses decreases problem. Combination called an Achromat. hite urce Blue Green Red

44 Achromatic Doublet Positive lens from crown glass Low dispersion Negative lens form flint glass High dispersion

45 Achromatic Doublet First lens stronger than second Pair are positive First lens focuses blue more strongly Second lens corrects for this Greater dispersion Only correct for two colours Usually red and blue If two close surfaces made same curvature Lenses can be cemented together.

46 Spherical aberration Edges of a lens refract light more then the centre. Most of the rays focus together to form a disc Called the circle of least confusion. Circle of least confusion Focus of outer rays Focus of inner rays

47 Coma Edge of lens different focal length to centre Rays at angle focused at different points Produces comet like image

48 Curvature of field Lens focuses on surface of a sphere. As object moves off the optical axis focal distance to the lens is farther. Gives either pin cushion or barrel distortion. minimised by the use of compensating lenses. Curved focal field

49 Distortion Off-axis magnification different from central magnification Pincushion or barrel distortion Object Barrel Pin cushion

50 Astigmatism

51 Stops A stop is an aperture in a system Often to reduce aberrations Aberrations greater at edge of lens Exit pupil Stop Entrance pupil Image f 1 Object lens 1 f 2 lens 2 f 1 f2

52 Entrance and Exit Pupil Entrance pupil Virtual image of stop by lens 1 Exit pupil Virtual image of stop by lens 2 Size of pupil depends on viewing direction Gives diameter of aperture of light for system

53 Resolution Ability to discern fine details. Expressed as a linear dimension. For typical electron microscope is ~ 0.2nm. Objects separated by >0.2nm will be resolved as being separate. Lord Rayleigh in 1896 first described resolution as a function of the Airy disc. Airy discs of two point light sources

54 Rayleigh Criterion Rayleigh: Limit of resolution Two light sources must be separated by at least the diameter of first dark band. Light distribution of a cross section of respective airy disc.

55 Abbé derived an expression for resolution Comes from size of the lens that captures light. Resolving power = 0.61 λ N.A. The resolution will be expressed in the same units as the wavelength of the light.

56 Depth of Field Area in front of and behind the specimen that will be in acceptable focus. Determined by numerical aperture. epth of field In focus Depth of field In focus

57 Depth of Field & Focus Depth of field concerns focus plane of specimen. D fi λ ( N.A. ) 2 Range of acceptable focus for the image is called depth of focus. = depth of focus depth of focus

58 Depth of Focus Nearly same as depth of field Determined by magnification as well. Higher magnification depth of field becomes shorter, higher magnification increase depth of focus for image. Depth of focus given by R.P. is the resolving power. D fo = M 2 R.P. N.A.

59 Size of image on retina depends on distance from eye Closest distance called near point. Varies with age and eye defects. Varies with age as lens becomes less flexible. 10 years old ~ 7cm 25 years old ~ 12 cm 45 years old ~ 28 cm 50 years old ~ 40 cm 60 years old ~ 100 cm 70 years old ~ 400 cm Normally given as 25 cm

60 Optical Instruments Viewed by Eye : Microscope L=16cm in general, 20X means that f = 16cm/20 = 8 mm

61 Optical Instruments : Telescope α ' M = = α telescope f f objective eyepiece

62 Waveguides Trapping Light by TIR