Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics1 Light Control through Optical System Our major concerns: field of view and image brightness We will learn: aperture, stop, aperture stop, field stop, pupil and window. The element in an optical system that determines the maximum cone of light passing through the system is called the aperture stop (AS). The limiting cone angle  1 is easy to obtain but  2 is not.

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics2 Light Control through Optical System A front stop serves as an aperture stop. Entrance pupil (E n P): the image of AS seen through the optical elements in front of it. Exit pupil (E x P): the image of AS formed by all imaging elements following it. E n P is conjugate with E x P.

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics3 Light Control through Optical System A rear stop behind the lens serves as the aperture stop (AS) and the exit pupil (E x P). A front stop serves as the aperture stop (AS) and the entrance pupil (E n P).

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics4 Light Control through Optical System Chief ray: a ray from object that passes through the axial point in E n P. The ray must also passes through the axial point of both the AS and E x P. Entrance and exit pupils are related to AS and govern the brightness of the image.

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics5 Light Control through Optical System The field of view describes the range of the object that can be viewed. The partial shielding of the outer portion of the image by stop S for off-axis object points is called vignetting. Excessive vignetting may make the image of a point object appear astigmatic. The field of view (object plane) is often defined as the circle (OU) that consisting of all object points having at least half the maximum irradiance found at the center of the image. Field stop (FS) limits the size or angular width of the object that can be imaged. Entrance window (E n W): the image of FS formed by all optical elements preceding it. Exit window (E x W): the image of FS formed by all optical elements following it.

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics6 Light Control through Optical System Example : Consider an optical system made up of two positive thin lenses with a stop S located between them as shown in the figure. (a) Locate the position and size of the final image. (b) Locate the AS, E n P, and E x P for the system. (c) Locate the FS, E n W, and E x W for the system. Solution: s 1 =  40 cm; f 1 =40/3 cm; s 1 =20 cm; s 2 =  10 cm; f 2 =20/3 cm; s 2 =20 cm;

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics7 Light Control through Optical System (b) Lens L1 is AS and E n P. Using thin lens equation, E x P is located 8.57 cm to the right of lens L2 with an diameter of 4/7 cm. (c) To find FS, we must determine the angles subtended at the center of the entrance pupil. The stop S is FS. E n W is located in the object plane with a diameter of 2 cm. E x W is located at the image plane with a diameter of 2 cm. A schematic eye:

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics8 Light Control through Optical System Homework: 1.Two positive lenses, each of diameter 5 cm and focal length 15 cm, are separated by a distance of 10 cm. For what range of object positions along the optical axis will (a) the first lens and (b) the second lens control the amount of light passing through the system? 2.An aperture of opening 5 cm in diameter is positioned 15 cm to the left of a positive lens of rim diameter 10 cm and focal length 12 cm. Each element is centered on the optical axis. (a) For an object located 6 cm to the left of the aperture, which element serves as AS? (b) Where are the entrance and exit pupils located? 3.An aperture of 5-cm opening is located 8 cm to the right of a positive lens of diameter 10 cm and focal length 12 cm. (a) For an object located 6 cm to the left of the lens, which element is AS? (b) Where is E n P? What is its size? (c) Where is E x P? What is its size? 4.An object measures 2 cm high above the axis of an optical system of a 2-cm AS and a thin convex lens of 5-cm focal length and 5-cm aperture. The object is 10 cm and the AS is 2 cm in front of the lens. Determine the position and size of the entrance and exit pupils, as well as the image. 5.An optical system, centered on an optical axis, consists of (left to right): object plane, thin lens L 1 30 cm from the object plane, aperture A 15 cm farther from L 1, thin lens L 2 10 cm farther from A, and image plane. Lens L 1 has a focal length of 10 cm and a diameter 6 cm; L 2 has a focal length of 5 cm and a diameter of 6 cm; aperture A has a centered, circular opening of 2.0 cm in diameter. Locate (a) image plane, (b) AS and E n P, (c) E x P and (d) FS, E n W and E x W.

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics9 Optical Instrumentation Prisms: generally not used alone Angular deviation: Minimum deviation occurs when the ray of light passes through the prism symmetrically. For small prism angle: Or: Ophthalmic Prisms: Small angle prisms are used in ophthalmology to correct double vision. When two eyes do not aim simultaneously at an object correctly, tow nonoverlapping images are perceived.

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics10 Optical Instrumentation Bending power of prism (prism diopter pd): measured in terms of the displacement y caused by the prism on a screen 1 m from the prism. For two thin prisms: Example: An ophthalmic prism of prism power P prism =2.5 is desired. If the prism material is of index n=1.56, what should be its apex angle? How should it be oriented to bend the ray downward from the horizontal? Solution: The apex angle should be about 2.6  with base downward.

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics11 Optical Instrumentation Example: A prism material has an index of 1.50 and apex angle of 5 . (a) What is the power of the prism? (b) By how much does it displace an incident ray at 60 cm? Solution: The ray is displaced 4.36 cm at a distance of 100cm. So it is displaced 2.6 cm at 60 cm. Example: Two small angle prisms, both base down, are used in combination. One has a power of 2.5 pd, the other of 4.4 pd. (a) What is the deviation angle of the pair? (b) What is the displacement at 100 cm from the pair? Solution: The displacement is 6.9 cm at 100 cm and is downward toward the base of the prism. Dispersion: angular spread Cauchy equation:

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics12 Optical Instrumentation Three specified colors are used: · C line (656.3 nm) from a hydrogen vapor lamp. · d line (587.2 nm) from a sodium lamp. · F line (486.1 nm) from a hydrogen vapor lamp. The refractive indices of substances for these three precise colors are denoted by n C, n d, and n F, respectively. Dispersive power: An instrument using a prism as a dispersive element, which is able to measure the angles of deviation of various wavelength, is called a prism spectrometer. D

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics13 Prisms may be combined to produce achromatic overall behavior, that is, the net dispersion D for two given wavelength may be made zero, even though the deviation is not zero. The direct vision prism accomplishes zero deviation for a particular wavelength while at the same time providing some dispersion. Optical Instrumentation achromatic prism For particular wavelength:

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics14 Camera: It forms a real, inverted image on a light sensitive surface by a converging lens. Below is a Zeiss Tessar system produces a flat, well-focused image over a large angular field. f-number (relative aperture), exposure E; exposure time Δt; and intensity I. If the f-number is 8, it is usually referred to f/8 by photographers. Optical Instrumentation

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics15 Depth of Focus The blur disc diameters PQ and RS are their maximum, above which blur would be noticed in an image in the planes PQ or RS. The distance between the blur discs is known as the depth of focus for the image B. It is increased with a smaller aperture. Optical Instrumentation

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics16 Depth of Field l1l1 l l2l2 l'2l'2 l'l' l'1l'1 + = Optical Instrumentation

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics17 Optical Instrumentation Example: A camera with a 5-cm focal length lens and f/16 aperture is focused on an object cm away. Allowing satisfactory quality of the image when d is 0.04 mm, what are the near and far distances and the depth of field? Solution: d=0.04 mm, f/D=16, f=5 cm, D=5/16 cm, l=  cm, near point: far point: The depth of field is 721 cm.

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics18 Angular Magnification The visual angle  is aided with the lens and  is the unaided angle. The angular magnification is dependent on the position of the observer’s eye (distance d). Optical Instrumentation

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics19 Nominal Magnification When the image is formed at infinity, M is referred to as the nominal magnification M nom. And is equal of one-quarter of the lens power. Eyepieces: The eyepieces, or ocular, of an instrument is fundamentally a magnifier. Its function is to view the image (called objective) formed by a lens or lens system preceding it in an optical instrument. Most types of eyepieces consist essentially of two lenses referred to respectively as the field lens (it increases the field of view) and the eye lens (is placed next to the observer’s eye). Optical Instrumentation

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics20 Huygens Eyepiece: The two lenses are separated by a distance equal to the average of their focal lengths. The function of the field lens is to deviate inward those rays which would otherwise have missed the eye lens, thus increasing the field of view. Huygens eyepiece reduces longitudinal chromatic aberration. Optical Instrumentation

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics21 Ramsden Eyepiece Ramsden eyepiece consists of two same plano-convex lenses, separated by about 2/3f. The final image is formed at infinity. The function of the field lens is to deviate towards the axis those rays which would otherwise miss the eye lens. This increases the field of view. Optical Instrumentation

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics22 Microscope The simplest form of microscope consists of two positive powered lenses: the objective (O-lens) which has a shorter focal length and the eyepiece (  -lens) which has a longer focal length. In normal use the final image is at the standard near point distance of 25cm from the  - lens. Optical Instrumentation

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics23 Microscope If the observer’s eye is emmetropic and unaccommodated, the final image must be formed at infinity instead of at the standard near point. This is achieved by withdrawing the  -lens slightly such that the primary image falls on the first focal plane of this lens. More prolonged viewing of the image is possible with less eye strain. Optical Instrumentation

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics24 Telescope The telescope is used to enlarge the image of a distant object. The figure shows the image formation by a Keplerian Astronomical Telescope. In normal usage the primary image also coincides with the first focal plane of the eyepiece. The equivalent power of the afocal configuration telescope is zero. The instrument enlarges the visual angle. Optical Instrumentation

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics25 Telescope The terrestrial telescope with an erector lens. With the erector lens, the telescope is longer but the image viewed is upright. The Galilean telescope with a diverging eyepiece. The final image is upright. Optical Instrumentation

Hong Kong Polytechnic University Optics 1----by Dr.H.Huang, Department of Applied Physics26 Optical Instrumentation Homework: 1.A parallel beam of white light is refracted by a 60  glass prism in a position of minimum deviation. What is the angular separation of emerging red (n=1.525) and blue (n=1.535) light? 2.Ophthalmic prisms of 2.0 and 3.0 pd are to be designed for the left and right lenses, respectively, of a pair of eyeglasses, in order to correct for a 5.0 pd misalignment in the vertical vision of a patient. The prism in the left lens is to produce a downward displacement of the light passing through it, while the prism in the right lens is to produce an upward displacement. The glass used for each lens has a refractive index of (a) What is the prism apex angle for each ophthalmic prism? (b) What is the orientation of the prism base in each lens? 3.A prism of 60  refracting angle gives the following angles of minimum deviation when measured on a spectrometer: C line, 38  20; D line, 38  33; F line, 39  12. Determine the dispersive power of the prism. 4.A camera is used to photograph three rows of students at a distance 6 m away, focusing on the middle row. Suppose that the image defocusing or blur circles due to object points in the first and third rows is to be kept smaller than a typical silver grain of the emulsion, say 1  m. At what object distance nearer and farther than the middle row does an unacceptable blur occur if the camera has a focal length of 50 mm and a f  number of f/4?