PHY385H1F Introductory Optics. Practicals Session 7 Studying for Test 2
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1 PHY385H1F Introductory Optics Practicals Session 7 Studying for Test 2
2 Entrance Pupil & Exit Pupil A Cooke-triplet consists of three thin lenses in succession, and is often used in cameras. It was patented in 1893, and was the first lens system that allowed elimination of most of the optical distortion or aberration at the outer edge of lenses. The focal lengths of a particular triplet are: f 1 = +12 cm, f 2 = 40 cm, and f 3 = +12 cm. Lens 2 is located 6 cm behind lens 1, and lens 3 is located 2 cm behind lens 2.
3 Entrance Pupil & Exit Pupil The focal lengths of a particular triplet are: f 1 = +12 cm, f 2 = 40 cm, and f 3 = +12 cm. Lens 2 is located 6 cm behind lens 1, and lens 3 is located 2 cm behind lens 2. An aperture stop of diameter 1.5 cm is located halfway between lens 2 and lens 3. All 3 lenses have diameters of 5 cm. What is the entrance pupil? What is the exit pupil?
4 Entrance Pupil The entrance pupil is the image of AS as formed by lenses 1 and 2, which precede it. To find the entrance pupil, you must trace the rays as going backwards (from right to left) through the optical system. For Lens 2, s o = 1 cm, f 2 = 40 cm. s i = 1 f 2 1 s 0 1 = = cm D 2 = M T D AS = s i D s AS = = cm o 1 Image of AS from lens 2 is cm in front of lens 2 with a diameter of cm.
5 Entrance Pupil The entrance pupil is the image of AS as formed by lenses 1 and 2, which precede it. For Lens 1, s o = = cm, f 1 = +12 cm. s i = 1 f 1 1 s 0 1 = = cm D en = M T D 2 = s i D s 2 = = cm o The entrance pupil is 16.7 cm to the right of lens 1, and has a diameter of 3.50 cm. Light from an object within a cone which would go through this entrance pupil will propagate through the system to the detector. (This determines image brightness.)
6 Exit Pupil The exit pupil is the image of AS as formed by lens 3, which follows it. For Lens 3, s o = 1 cm, f 3 = + 12 cm. s i = 1 f 3 1 s 0 1 = = cm D ex = M T D AS = s i D s AS = = cm o 1 The exit pupil is 1.09 cm to the left of lens 3, and has a diameter of 1.64 cm. This determines the angular size of the cone of light which actually hits the detector.
7 Discussion Question.. Two plane mirrors form a right angle. How many images of the ball can you see in the mirrors?
8 Discussion Question air water A fish swims below the surface of the water. An observer sees the fish at: 1. a greater depth than it really is. 2. its true depth. 3. a smaller depth than it really is.
9 Discussion Question air water A fish swims directly below the surface of the water. An observer sees the fish at: 1. a greater depth than it really is. 2. its true depth. 3. a smaller depth than it really is.
10 Discussion Question f What will happen to the rays emerging to the right of the lens if the face is moved a little closer to the lens? 1. They will remain parallel. 2. They will diverge (spread out). 3. They will converge (toward a focus).
11 Discussion Question f What will happen to the rays emerging to the right of the lens if the face is moved a little further away from the lens? 1. They will remain parallel. 2. They will diverge (spread out). 3. They will converge (toward a focus).
12 Which distance is the Diameter, D, of the Lens? x 1 x 4 x 2 x 3
13 Which distance is the Focal Length, f, of the Lens? x 1 x 4 x 2 x 3
14 Which distance is the Radius of curvature, R 1 or R 2, of the Lens? x 1 x 4 x 2 x 3
15 You take a picture of a tree, using an exposure time of Δt. The distance to the tree, s o, is fixed. If you keep D and f fixed, but increase Δt, what will change about the well-focussed image on the detector? 1. It will get fainter (less energy per pixel). 2. It will get brighter (more energy per pixel). 3. It will have the same exposure level. A Simple Camera: s o s i Object Aperture, inner diameter D Detector Lens, focal length f
16 You take a picture of a tree, using an exposure time of Δt. The distance to the tree, s o, is fixed. If you keep f and Δt fixed, but increase D, what will change about the well-focussed image on the detector? 1. It will get fainter (less energy per pixel). 2. It will get brighter (more energy per pixel). 3. It will have the same exposure level. A Simple Camera: s o s i Object Aperture, inner diameter D Detector Lens, focal length f
17 You take a picture of a tree, using an exposure time of Δt. The distance to the tree, s o, is fixed. If you keep D and Δt fixed, but increase f, what will change about the well-focussed image on the detector? 1. It will get fainter (less energy per pixel). 2. It will get brighter (more energy per pixel). 3. It will have the same exposure level. A Simple Camera: s o s i Object Aperture, inner diameter D Detector Lens, focal length f
18 You take a picture of a tree, using an exposure time of Δt. The distance to the tree, s o, is fixed. If you increase the focal ratio f/d, but wish to keep the same exposure, how should you adjust Δt? 1. Increase Δt 2. Decrease Δt 3. Keep the same exposure time. A Simple Camera: s o s i Object Aperture, inner diameter D Detector Lens, focal length f
19 What determines data speed? Broadband networks deliver speeds of 100Mbps (108 bits per second) A bit is a zero or a one To increase data speed over a line, you should 1. Increase the speed, in m/s of signals going through the line 2. Decrease the time between bits (in s) 3. Both 1 and 2
20 Hyperopia (far-sightedness) To focus an image of the object which is 25 cm away, the positive focusing power of the eye must be 1. Increased 2. Decreased
21 Myopia (near-sightedness) To focus an image of the object which is at infinity, the positive focusing power of the eye must be 1. Increased 2. Decreased
22 Crossing the street You are crossing the street, and you look to your left. You either see Car A or Car B. What do you think is the difference? B A 1. Car B is bigger 2. Car B is closer 3. It is impossible to tell without further information
23 What is the focal length of a magnifier which has POWER 3x? 1. 3cm 2. 8 cm cm cm
24 Compound Microscope Example A microscope has an eyepiece with focal length f e = 3.0 cm, and an objective lens with focal length f o = 2.0 cm A bacterium is viewed with the microscope. Assuming this is a standard tube length microscope, what is the image distance s i of the real image of the bacterium formed by the objective lens? cm cm cm cm cm
25 Lens Magnification f h o h i s o s i What is the transverse magnification of the image M T = h i /h o? 1. f/s i 2. 1/f 3. (s i + s o )/f 4. s o /s i 5. s i /s o
26 Pinhole Magnification h o h i s o s i What is the transverse magnification of the image M T = h i /h o? 1. s o /s i 2. s i /s o
27 Pinhole vs. Lens h o h i s o s i What is the advantage of a lens camera as opposed to a pinhole camera? 1. Sharper focus 2. Greater depth of field 3. Greater magnification 4. Brighter image
28 Absorption Coefficient What are the absorption coefficients α λ for a perfect mirror and a perfectly white piece of paper? 1. 1 for the mirror, 1 for the paper 2. 0 for the mirror, 1 for the paper 3. 1 for the mirror, 0 for the paper 4. 0 for the mirror, 0 for the paper
29 Stefan-Boltzmann Law The filament of a 10-Watt light bulb has a temperature of 1750 degrees Kelvin. If, instead, it is operated at 3500 degrees Kelvin, what will be the power of the bulb? W W W W
30 Wien s Law The maximum wavelength of the spectrum from a 10-Watt light bulb is 1,600 nm (infrared), when its temperature is 1750 degrees Kelvin. If, instead, it is operated at 3500 degrees Kelvin, the maximum wavelength of its spectrum will be 1. 3,200 nm nm nm nm
31 Boltzmann Distribution Consider a tank of Hydrogen gas at room temperature (20 degrees Celsius). Hydrogen has a famous red transition n = 3 2 which has a wavelength of 656 nm. (Astronomers call this H-alpha.) What is the ratio N 3 /N 2? In this picture, the temperature of the Hydrogen gas is 7000 K. Ground state H-atoms are not shown. What do you think? 1. Black dots represent atoms in the n=2 state, white dots represent atoms in the n=3 state 2. White dots represent atoms in the n=2 state, black dots represent atoms in the n=3 state
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