PHY385H1F Introductory Optics
Practicals Session 7 Studying for Test 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: f1 = +12 cm, f2 = – 40 cm, and f3 = +12 cm. Lens 2 is located 6 cm behind lens 1, and lens 3 is located 2 cm behind lens 2. Entrance Pupil & Exit Pupil
• The focal lengths of a particular triplet are: f1 = +12 cm, f2 = – 40 cm, and f3 = +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 half- way between lens 2 and lens 3. All 3 lenses have diameters of 5 cm. • What is the entrance pupil? What is the exit pupil? 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, so = 1 cm, f2 = – 40 cm. 1 1 −1 1 1 −1 푠푖= − = − = −0.97561 cm 푓2 푠0 −40 1
푠푖 0.97561 퐷2 = 푀푇 퐷퐴푆 = − 퐷퐴푆 = 1.5 = 1.4634 cm 푠표 1
• Image of AS from lens 2 is 0.97561 cm in front of lens 2 with a diameter of 1.4634 cm. Entrance Pupil • The entrance pupil is the image of AS as formed by lenses 1 and 2, which precede it.
• For Lens 1, so = 6 + 0.97561 = 6.97561 cm, f1 = +12 cm. 1 1 −1 1 1 −1 푠푖= − = − = −16.6602 cm 푓1 푠0 12 6.97561
푠푖 16.6602 퐷푒푛 = 푀푇 퐷2 = − 퐷2 = 1.4634 = 3.49511 cm 푠표 6.97561 • 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.) Exit Pupil • The exit pupil is the image of AS as formed by lens 3, which follows it.
• For Lens 3, so = 1 cm, f3 = + 12 cm.
1 1 −1 1 1 −1 푠푖= − = − = −1.0909 cm 푓3 푠0 12 1
푠푖 1.0909 퐷푒푥 = 푀푇 퐷퐴푆 = − 퐷퐴푆 = 1.5 = 1.6364 cm 푠표 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. Discussion Question.. Two plane mirrors form a right angle. How many images of the ball can you see in the mirrors? 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. 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. 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). 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). Which distance is the Diameter, D, of the Lens?
x4 x1
x3 x2 Which distance is the Focal Length, f, of the Lens?
x4 x1
x3 x2 Which distance is the Radius of curvature, R1 or R2, of the Lens?
x4 x1
x3 x2 A Simple Camera:
so si
Object
Aperture, inner Detector diameter D Lens, focal length f You take a picture of a tree, using an exposure time of Δt. The
distance to the tree, so, 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:
so si
Object
Aperture, inner Detector diameter D Lens, focal length f You take a picture of a tree, using an exposure time of Δt. The
distance to the tree, so, 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:
so si
Object
Aperture, inner Detector diameter D Lens, focal length f You take a picture of a tree, using an exposure time of Δt. The
distance to the tree, so, 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:
so si
Object
Aperture, inner Detector diameter D Lens, focal length f You take a picture of a tree, using an exposure time of Δt. The
distance to the tree, so, 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. 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 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 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 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 www.magnifier.com
What is the focal length of a magnifier which has “POWER 3x”? 1. 3cm 2. 8 cm 3. 16 cm 4. 25 cm Compound Microscope Example • A microscope has an eyepiece with focal length fe = 3.0 cm, and an objective lens with focal length fo = 2.0 cm • A bacterium is viewed with the microscope. • Assuming this is a standard tube length microscope, what is the image distance si of the real image of the bacterium formed by the objective lens? 1. 2.0 cm 2. 3.0 cm 3. 14 cm 4. 16 cm 5. 18 cm
Lens Magnification 푓
ℎ표
ℎ푖
푠표 푠푖
What is the transverse magnification
of the image MT = hi/ho? 1. − f/si 2. − 1/f 4. −so/si 3. −(si + so)/f 5. − si/so Pinhole Magnification
ℎ표
ℎ푖
푠표 푠푖
What is the transverse magnification
of the image MT = hi/ho? 1. −so/si 2. − si/so Pinhole vs. Lens
ℎ표
ℎ푖
푠표 푠푖 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
Absorption Coefficient
• What are the absorption coefficients 훼휆 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 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? 1. 20 W 2. 100 W 3. 160 W 4. 400 W 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 2. 800 nm 3. 100 nm 4. 400 nm 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 N3/N2? 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