Ch 24 Optical Instruments 講者： 許永昌 老師

Contents Lenses in combination The Camera Vision Optical Systems That Magnify Magnifier Microscope Telescope The Resolution of Optical Instruments Aberration Diffraction resolution

Lenses in Combination (請預讀P739~P741) Purpose: Improve the image quality. Rule: The image of the first lens acts as the object for the second lens. Objective lens (接物鏡, bigger) and eyepiece (接目鏡, smaller)

Lenses in Combination (continue) 1st Lens (objective) 1st Lens  2nd Lens s’1 s2, h’1=h2. 2nd Lens (eyepiece) mnet=h’2/h1=m1m2.

Exercise (I need three students) The focal length of lens A is 12cm. If I put an object 30cm from the center of this lens, where is the position of the image? Lateral magnification? (DEMO) The focal length of lens B is 3cm. If I put an object 4cm from the center of this lens, where is the position of the image? Lateral magnification? (DEMO) Combination of these two lenses as shown in follows. Where is the position of the image? Lateral magnification? 30. cm 24. cm ? cm

The Camera (請預讀P742~P745) In this part, you will learn The configuration of a Camera. How to change the effective focal length by a combination lenses. f-number (a dimensionless number,  f ). How to calculate lateral magnification. The relation between Intensity and f-number. How do a digital camera work?

The camera (continue) It consists of Lens (lenses): Focus the image on the detector. f ~6mm  ~18mm. Stop to think: m=-s’/s ~ -f/s when s > 10f. Aperture + shutter: Control the exposure (intensity and the energy per area). Dtshutter~ 1/1000 s  ~ 1/30 s. f-number  f/D. D: the diameter of the aperture. Stop to think: Why Detector: Electronic light-sensitive surface called charge-coupled device (CCD).

The Camera (continue) Change the effective focal length: Note: The approximation we used here is that s when s > 10f. Reason: Action: Two students hold two lens and change the distance between these two lenses. Observe the change of the position of real image.

The Camera (continue) Aperture: Shutter: Their combination: Control the intensity. IdetectorD2. Shutter: Control the exposure time. Their combination: Control the exposure (energy) per area. I=P/A  1/m2  1/f 2. Side view Front view The same power

Camera (continue) f-number: Notation: E.g. 1/125 F5.6 e.g. f-number = 4.0. f/4.0. F4.0. E.g. 1/125 F5.6 Shutter time: 1/125 s f /D=5.6.

The Camera (final) The detector of a digital camera is charge-coupled device ( CCD ).

Homework Student Workbook 1,2, 4, 5

Vision (請預讀P745~P748) In this part you will learn The configuration of a human eye and the function of each part. Far point and near point. Vision defect and their correction. Think of that: Find the correspondence between a human eye and a camera.

Vision (continue) The configuration of a human eye: Note: Cornea + Aqueous humor: lens in a Camera Lens: Adjust the focal length. Think of that: 1. f-number of a human eye. 2. Why do everything will be very blurry if we open our eyes underwater? ~2.4 cm n=1.34 n=1.44 n=1.34 1.5 ~ 8 mm

Vision (continue) Far point (FP) and Near point (NP): Action: The farthest distance a relaxed eye can focus. Typical: ~ 25 cm. Near point (NP): The closest distance at which an eye can focus, using maximum accommodation. Typical:  m. Action: Find NP of your eyes.

Vision (final) Vision defects: Correction: Presbyopia (老花眼) --- edge, loss of accommodation. Hyperopia (遠視) --- shortened eyeball. Myopia(近視) --- Elongated eyeball. Correction: By an extra lens: The power of a lens: 1/f.(這不是功率) Diopter (屈光度): D: 1D= 1 m-1. nD=n*100度。 所以，近視的人都有??可用。

Homework Student Workbook 6, 7

Optical Systems That Magnify (請預讀P749~P753) In this part you can learn The concept of magnification for our eyes. The function of a magnifier. How do microscopes and telescopes work? Stop to think: If the lens’s focal length is f and the incident angle is q, please tell me the position and height of image. q h’ s’

Angular size and magnification We feel that something is magnified  the real image on the retina is magnified  angular size is magnified. Example: Dmoom=3.48*106 m. dmoon to earth= 3.84*108m. q=D/d~ 0.01 rad Your arm ~ 1m; your thumbnail ~ 1cm. Therefore, the easiest way to magnify an object is that …………………??? Get closer.

Magnifier However, we cannot focus on the object if it’s closer than your near point. it depends on the object’s height. Magnifier: Enhance the angular size. The virtual image of a converging lens. Angular magnification: (簡言之，與肉眼所能看的最大放大率比) M  q/qNP. Think of that: 如果眼睛貼著透鏡看s < f 的物體呢？會如何? Hint: 角度&NP. f > NP. f < NP. M of a magnifier is defined while s~f  .

The Microscope and Telescope The eyepiece is used as a simple magnifier to view the image made by an objective lens. Microscope: Telescope:

Homework Student Workbook 8, 9

The resolution of Optical Instruments (請預讀P753~P756) Since M=25 cm/f for a magnifier, it seems that we can use a single magnifier whose f is short enough as a microscope. However, it is not true. Two limitations: Any lens has dispersion: Chromatic aberration (frequency) Spherical aberration (angle) Diffraction: The pattern of a parallel light focus on the lens’s focal point is a diffraction pattern; therefore it will be a spot instead of a point.

Diffraction again Mechanism: A lens both focuses and diffracts light waves. These two effects are separable. The minimum spot size is It becomes a limit of photolithography in the manufacturing of integrated circuits. Usually f  D for realistic lens  wmin 2.5l. If the mask is projected with ultra-violet light having l~200nm, then the smallest elements on a chip are about 0.50 mm wide.

Resolution Telescope: Microscope: Rayleigh’s criterion: The two objects are resolvable if a > qmin=1.22l/D. The two objects are not resolvable if a < qmin. The two objects are marginally resolvable if a = qmin. Microscope: 不證。 Stop to think: “看”得到原子嗎？

Homework Student Workbook Student Textbook 10, 11 Student Textbook 27, 30, 31 請自行製造本章的 terms and notation 的卡片。