Sketch the light paths from object to image in a single lens system in following situations.

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Leona Rice
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1 Solutions o Chapter I 1.1. There are three rules governing light path or a simple lens: 1) light ray passing through the center o a lens is not deviated. ) Light ray parallel with optic axis will pass through the rear ocal point. 3) ray passing through the ront ocal point will be reracted in a direction parallel to the axis. Sketch the light paths rom object to image in a single lens system in ollowing situations. a) a < ; b) a = ; c) > a > ; d) a = ; and e) a >. a is distance o object rom lens and, is ocal length o lens. By this exercise, you may understand that > a > is necessary to obtain a real magniied image. a) image B B O p a p is the distance o image rom lens. b) no image c) B B O a p 1

2 d) e) B a O p B 1.. The work distance between the specimen and objective lens is determined by magniications o the lens (M). Estimate the dierence in the work distance or objective lens with power o 5X, 0X and 50X. ν M = u = = + u ν M + 1 M Where u represents the work distance o the lens; v is the distance between image and lens. or M = 5, 6 u = ; or M = 0, 5 1 u = ; or M = 50, 0 51 u =. 50 Note that the ocal length o lens decreases with its power. u > u > u. Thus, 5X 0X 50X 1.3. Calculate the resolution and the depth o ield o the objective lenses o light microscope. We know the reractive index o vacuum is 1, and that o air can be treated as 1. ssume the blue light is used in the microscope.

3 Magniication/N 5 X / X/ X / X / X / 0.90 The wavelength ( λ ) o blue light is nm, sinα 1.λ R= ;tan a= ; D ; = N 1 sin α Ntanα or 5X/0.13, or 10X/0.5, or 0X/0.40, or 50X/0.70, or 100X/0.90, R = = =.μ m, N D = = 34.0μ m; 0.13 / R = = = 1. μ m ; N D = = 9.0μ m. 0.5 / R = = = 0.7 μ m; N D = = 3.3μ m / R = = = 0.41 μ m; N D = = 0.84μ m / R = = = 0.3 μ m; N D = = 0.31μ m 0.90 / Compare resolution and depth o ield o light microscopes and electron microscopes. The wavelength o electrons is nm (100 kv) and the angle α o electron microscope is 0.1 radians. or electron microscopes, as α is very small, α sinα tanα, 3

4 e α sinα tan α, Re = = 0.03nm N D e = 0.45nm. 0.1, or light microscope, assume the average wavelength o light, the wavelength is about 560 nm and α Rl = = = nm 0.48μ m, N sin D e = = nm 0.97μ m. sin 45 tan 45 We can see that the resolution o electron microscopes is much higher than that o light microscopes. However, the depth o ield o electron microscopes is much smaller than that o light microscopes We have samples o an annealed l alloy and an annealed plain carbon steel to be examined. The polishing area o samples is about 5 mm x 3 mm. a. To avoid the plastic deormation in the surace layer, what are the maximum compression orces should be used or polishing the samples o annealed l alloy and the plain carbon steel, respectively? b. I the normal compress orce cannot cause the plastic deormation, what kind o loading on samples more likely cause plastic deormation? Yield strength o annealed l alloy = 150 MPa Tensile strength o annealed l alloy = 400 MPa Yield strength o annealed plain carbon steel = 400 MPa Tensile strength o annealed plain steel = 700 MPa a) or the annealed l alloy specimen, the maximum compression orce without plastic deormation, Pmax = σ ys = = 50N ; or the annealed plain carbon specimen, the maximum compression orce, Pmax = σ ys = = 6000N; Where σ ys is yield strength, and is the polishing area o samples. b) Plastic deormation o specimen may results rom shear stress exerted during polishing. Materials CharacterizationYang Leng 008 John Wiley & Sons (sia) Pte Ltd 4

5 1.6. To obtain a 400X magniication image we may choose 40X objective lens and 10X projective lens or 0X objective lens and 0X projective lens. What are dierences in their image quality? The objective lens is the most important optical component o a light microscope. It generates the primary image o the specimen, and its resolution determines the inal resolution o the image. The projective is or enlarging a primary image ormed by the objective so than eyes can see a micro-object comortably. Using an objective lens with a higher power will produce an image with a higher real magniication o image than that o using higher power projective lens Describe specimen preparation procedure or examining a. cross-section o metal needle b. coating layer on metal substrate c. lead-tin solder d. polyethylene blended with other crystalline polymer a. The technique should make sure that the cross section is perpendicular to surace o the polishing medium. (i) metal needle is sectioned by diamond saw or electronic discharge machining (EDM). (ii) clamp to hold the needle uprightly, and then mounted in either epoxy resin and or thermosetting powder. (iii) Hand or machine grind the specimen on the abrasive paper (40,30,400,600-grit) with running water supplied to cool the specimen suraces. (iv) Polish the specimen to remove all visible scratches rom grinding with rotating polishing wheel. (v) Select the suitable etchant, temperature and time to etch the specimen. b. The techniques should make sure that the coating section will not be ground or polished away. (i) Section the specimen by diamond saw, and hal the specimen along the direction perpendicular to the coated surace. (ii) Put the two halves together with coating aces each other beore mounting. The rest procedure is similar to those in a. c. Polishing the sot metal specimen should careully avoid plastic deormation during grinding and polishing. The ollowing method can be used. (i) Make the specimen surace small. (ii) dd hard metal peas around the specimen beore mounding. 5

6 d. The polymer specimens are usually examined in transmitted light microscopes, by section them with microtomy. Phase contrast and luorescence-labeling techniques are commonly used Which parts o specimen will be highlighted under dark ield illumination in optical microscopic study i the specimen is a polycrystalline metal with a ew ceramic particles? The grain boundaries and ceramic particles will be highlighted under dark ield illumination Why do we rotate analyzer when examining microstructure with polarized light? When examining microstructure with polarized light, the light ray is split into two polarized light waves vibrating in two planes perpendicular to each other. The phase dierence o two polarized light waves creates a resultant light. Rotation o the analyzer through 360 o will result in light intensity change with direction in the specimen. Nature o the light intensity change relies on the phase dierence created in the specimen Why do we say that the Nomarski contrast may not provide a real three dimensional image? The Nomarski contrast results rom the phase dierence between two parallel polarized beams. The phase dierence generated in a specimen may or may be rom the surace relieves Why is the luorescence microscopy more commonly used in biological and polymer specimens than in metals and ceramics? The luorescence microscopy relies on the selective staining specimen with luorescent dyes. The luorescent dyes can well diuse into biological or polymeric materials, not into metals and ceramics.. 6

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