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Optics Practical - Lenses & Microscopes (on-campus version) This practical applies some key concepts of optics, such as focal length and the ideal lens equation, with an emphasis on understanding how a compound microscope works. Specific objectives of this practical are to help you to: • develop your ability to perform experiments, measure, record, analyse and interpret experimental data; ● make measurement of magnification of various optical devices, such as simple lenses, magnifying glasses and a compound microscope; • develop you understanding of optics to aid vision. Introduction Optical systems of interest in the biomedical sciences largely derive from very basic physics of refraction and the applications of lenses and optical fibres. In this practical you will observe the behaviour of light in simple optical systems and the eye, including magnification. An ideal lens is modelled by the equation: 1 1 1 = +== P i 0 where fis the focal length, o and i are distances of object and image, respectively, from the lens. P is referred to as the "power" of the lens when the distances are given in metres. P has the units of Dioptres or D, with 1 D = 1 m¹. (Note that the simple lens equation is only strictly true for "thin" lenses and when the object is on the axis.) 1 不 3 F₂ F₁ 2 ←----0--——. Simple diagram illustrating the Lens Equation for a converging lens. The behaviour of three characteristic rays are shown in the diagram above, where O is the object, I is the image, F1 and F2 are focal points located a distance f from the lens and ho and h; are the object and image heights. The lateral magnification, m, is defined by: image height hi object height ho m = i 0 = h. 0 ✓ <--f
For an inverted image, h, is taken as negative and the magnification is also negative. Note: In the lecture notes and some textbooks, symbols do and d, are used for distances o and i, respectively. For real objects o is positive and for real images t is positive. Light rays pass through real objects and images. In-class work Equipment When assembled, the apparatus should be arranged similarly to this: At the end of class please ensure all equipment has been returned to where you found it, in the same condition in which you found it. Report any malfunctioning equipment, or breakages, to a member of staff so we can replace it and/or send it for repair. Optical rail - allows optical components to be lined up such that distances can be easily measured. Lens holder - holds the lens and fits on optical rail Lens focuses light Slides - allows you to create an image that projects along the rail. Picture shows a grid slide, and there is also an arrow slide shown below. Lamp - light source that fits on optical rail. Also has room for slides to be placed in front of the bulb. (Photo includes a removable slide with a picture of an arrow.) Screen with graph paper - reflects the image from the rail (so you can see it without placing your eye at the end of the rail) Transformer - to supply power for the lamps (the 240V 'mains' from the standard sockets is too high for these bulbs). Part A. Focal Length and Magnification for a Convex Lens (-15 min) Purpose of this activity: To estimate and measure the focal length of a lens. To understand the magnification of a convex lens as a model of a microscope objective lens. Procedure 1. Estimate the focal length by focusing a very distant object (a window or light globe) onto a screen or wall. Record this value on your worksheet. 2. Using the lamp (with illuminated arrow slide), optical bench, lens holder and lens. measure the object distance o and the image distance i for a sharply focused image. Set the object to lens distance, o, to 20 cm. Move the screen to find a sharply focused image. Record the values in the table on your worksheet. From the measured o and i, calculate the focal length, f, of the lens and record this on the same table. Repeat the
Part C. Compound Microscope (~30 min) Purpose of this activity: To understand how a compound microscope works based on knowledge of the magnification of a lens and magnifying glass. Theory A model microscope may be made using two lens, L₁, the objective lens, and L2, the eyepiece lens (see the diagram below). In this practical both lenses have a focal length 10 cm, but in a typical microscope the objective lens has a must shorter focal length than the eyepiece lens. The objective lens L₁ forms a real image I₁ and the eyepiece lens L2 (having I₁ as its object) forms a virtual image (I₂), which is seen by the eye. The image I₁ must be inside and close to the focal plane of lens L₂ in order for this lens to act as a simple magnifier. S 3 пот F2 L1 [2 $932 Compound microscope. The objective lens L₁ produces a real image with lateral magnification of m₁; the eyepiece acts like the magnifying glass and has a magnifying power M2. The overall magnification of the microscope is: M = m₁ X M₂ For relaxed vision, I₁ is at F2, the focal plane of lens L2. Procedure 1. Consider the arrangement of lenses for the compound microscope in the diagram above. Knowing the magnification for relaxed vision, which can be found under the Theory section of Part B. Magnifying Glass, previous to this part, derive an expression for the overall magnification of the compound microscope in terms of the focal length, f1, of the objective lens L₁, the focal length, f2, of the eyepiece lens L1, and the distance, s, between the focal points of the two lenses (the distance between F'1 and F2 in the diagram). 0 L2
2. Construct a microscope, as in the diagram above, using two 10 cm focal length lenses. Place the illuminated arrow 15 cm from the objective lens. Calculate the position of I₁ and check the image is at the calculated location using the screen. If the image is not sharp, re-check your calculation and, if necessary, adjust the object position so the image is sharp at the calculated position. 3. For relaxed vision, where should the eyepiece lens L₂ be in relation to the image from the objective lens I₁? Place the eyepiece lens accordingly. 4. Estimate the magnifying power of the compound microscope with the same method as for the magnifying glass. Use the graph-paper slide in place of the arrow slide. You will probably find it hard to focus simultaneously (with different eyes) on the image at infinity and the reference screen. (It may help to place the disc with a small aperture in front of the lens in order to improve the depth of field and hence assist in focusing.) 5. Using the expression found in step 1, calculate the overall magnification based on the distances in the optical set-up. Compare this calculated value with the estimated maximum magnification in step 2. Do the two results agree? Explain why or why not.
Part C. Compound Microscope (8 marks total) 1. (2 marks) Derivation of expression for the overall magnification of the compound microscope. State any assumptions. 2. (1 mark) Calculated position of image of objective lens (cm):30 cm 3. (1 mark) Where should lens L₂ be placed with respect I₁? 4. (1 mark) Estimate of the magnification of the compound microscope set-up: 5. (3 marks) Using the expression in step 1, calculate overall magnification. Show your calculation. Compare this theoretical value with the estimated magnification in step 4. Do the two fesults agree? Explain why or why not. S=20