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Optics Start with a Point Source of Light

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Optics Start with a Point Source of Light Optics Start with a point source of light Photographic plate object We do not get a sharp picture of the source; we just get a diffuse blur The lens Rays get bent downwards object image Outer rays bend more Middle ray goes straight through If we arrange the shape of the lens just right, the rays will focus to a point Question: If we make the lens so that an object at A focuses, then will objects at B, C, ... focus somewhere as well? B C A A' Answer: No, they will not ... at best we can manage a good approximation .... The approximation (a) The lens in thin compared to the distances of the object and image small (b) The objects are small compared to the curvature radius of the lens surfaces curvature radius of lens surface small All the concerned rays have angles to the horizontal that are small Why do the rays bend ? sin ✓1 n2 Snell's law = sin ✓2 n1 n1 ✓1 The ray bends closer to the normal when it enters a denser medium n2 ✓2 n1 ✓1 The path of light rays is n always reversible 2 ✓2 The ray bends away from the normal when it enters a rarer medium GR9677 38 GR9677 sin ✓ 1 = sin 90o 1.33 n1 =1 sin ✓ 0.75 ⇡ n2 =1.33 ✓ 38 98. Suppose that a system in quantum state i has energy Ei . In thermal equilibrium, the expression -EkTi / Â Eei i -EkT/ Â e i i represents which of the following? (A) The average energy of the system (B) The partition function (C) Unity (D) The probability to find the system with 97. A beam of light has a small wavelength spread energy Ei d l about a central wavelength l . The beam (E) The entropy of the system travels in vacuum until it enters a glass plate at an angle q relative to the normal to the plate, as 99. A photon strikes an electron of mass m that is shown in the figure above. The index of refraction initially at rest, creating an electron-positron pair. of the glass is given by n()l . The angular spread The photon is destroyed and the positron and two dq ¢ of the refracted beam is given by electrons move off at equal speeds along the initial direction of the photon. The energy of the 1 (A) dq¢ = dl photon was GR0177 n 98. Suppose that a system in quantum state i 2 (A) mc has energy Ei dn. In()l thermal equilibrium, the (B) 2mc2 (B) dq¢ = dl expression dl (C) 3mc2 2 Ee-EkTi / (D) 4mc 1 Âdl i 2 (C) dq¢= i dl (E) 5mc l dn -EkT/ Â e i sin qi dl (D) dq¢ = sin q l represents which of¢ the following? (A) The averagetan energyq ¢ dn() lof the system (E) dq¢ = dl (B) The partitionn functiondl (C) Unity (D) The probability to find the system with 97. A beam of light has a small wavelength spread energy Ei d l about a central wavelength l . The beam (E) The entropy of the system travels in vacuum until it enters a glass plate at an angle q relative to the normal to the plate, as 99. A photon strikes an electron of mass m that is shown in the figure above. The index of refraction initially at rest, creating an electron-positron pair. of the glass is given by n()l . The angular spread The photon is destroyed and the positron and two dq ¢ of the refracted beam is given by electrons move off at equal speeds along the initial direction of the photon. The energy of the 1 (A) dq¢ = dl photon was n 2 (A) mc dn()l (B) 2mc2 (B) dq¢ = dl dl (C) 3mc2 Unauthorized(D) 4mc2 copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. 1 dl (E) 5mc2 (C) dq¢= dl l dn 66 sin q dl (D) dq¢ = sin q ¢ l tan q ¢ dn()l (E) dq¢ = dl n dl Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. 66 98. Suppose that a system in quantum state i has energy Ei . In thermal equilibrium, the expression -EkTi / Â Eei i -EkT/ Â e i i represents which of the following? (A) The average energy of the system (B) The partition function (C) Unity (D) The probability to find the system with 97. A beam of light has a small wavelength spread energy Ei d l about a central wavelength l . The beam (E) The entropy of the system travels in vacuum until it enters a glass plate at an angle q relative to the normal to the plate, as 99. A photon strikes an electron of mass m that is shown in the figure above. The index of refraction initially at rest, creating an electron-positron pair. of the glass is given by n()l . The angular spread The photon is destroyed and the positron and two dq ¢ of the refracted beam is given by electrons move off at equal speeds along the initial direction of the photon. The energy of the 1 GR0177 (A) dq¢ = dl photon was 98. Suppose that an system in quantum state i (A) mc2 has energy E . In thermal equilibrium, the idn ()l (B) 2mc2 expression(B) dq¢ = dl dl (C) 3mc2 Ee-EkTi / (D) 4mc2 1 Âdl i (C) dq¢= i dl (E) 5mc2 l dn -EkTi / Â e sin qi dl (D) dq¢ = represents whichsin qof¢ thel following? (A) The average energy of the system tan q ¢ dn()l (E) dq¢ = dl (B) The partitionn functiondl (C) Unity (D) The probability to find the system with 97. A beam of light has a small wavelength spread energy Ei d l about a central wavelength l . The beam (E) The entropy of the system travels in vacuum until it enters a glass plate at an angle q relative to the normal to the plate, as 99. A photon strikes an electron of mass m that is shown in the figure above. The index of refraction initially at rest, creating an electron-positron pair. of the glass is given by n()l . The angular spread The photon is destroyed and the positron and two dq ¢ of the refracted beam is given by electrons move off at equal speeds along the initial direction of the photon. The energy of the 1 (A) dq¢ = dl photon was n 2 (A) mc dn()l (B) 2mc2 (B) dq¢ = dl 2 dl (C) 3mc 2 Unauthorized(D) 4mc copying or reuse of 1 dl any part of this page is illegal. (C) dq¢= dl (E) 5mc2 GO ON TO THE NEXT PAGE. l dn 66 sin q dl (D) dq¢ = sin q ¢ l tan q ¢ dn()l (E) dq¢ = dl n dl Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. 66 What shape of then lens will do this job ? Where do the rays focus? small object large If the object if very far away, and we are looking at a small transverse region near the lens, the the rays look almost parallel focal point focal length f Rays from infinity focus at the focal point f If the object comes closer, then it is harder to focus the rays, so the image forms further away object distance o image distance i 1 1 1 + = o i f f 1 1 1 + = o i f object distance o image distance i f Object moves from infinity to focal point Image moves from focal point to infinity Magnification How do we locate the image of a point off the axis ? We rotate the rays object height h image height h 0 object distance o image distance i image height h 0 image distance i (a) Size is given by = object height h object distance o (b) The image is inverted h0 i We write = h − o HRW 28E: The sun subtends an angle of 0.5 degrees. You produce an image of the sun on a screen, using a convex lens of focal length 20 cm. What is the diameter of the image ? HRW 28E: The sun subtends an angle of 0.5 degrees. You produce an image of the sun on a screen, using a convex lens of focal length 20 cm. What is the diameter of the image ? 1 1 ∆✓ 0.50 radians ⇡ ⇡ 2 57 rays from top of object Diameter f ∆✓ 0.18 cm ⇡ ⇡ o image distance i = f rays from bottom of object Two lenses focal length f 1 focal length f 2 final image object height h height h 00 image height h 0 object distance o image distance i object distance o 0 image distance i 0 1 1 1 1 1 1 + = + = o i f1 o0 i0 f2 h h h Magnification M = 00 = 0 00 h h h ✓ ◆ ✓ ◆✓ 0 ◆ i i0 i i0 Final image is = = −o −o o o upright ✓ ◆✓ 0 ◆ ✓ ◆✓ 0 ◆ HRW A beam expander is made of two lenses as shown. What is the ratio of the intensities of the emergent beam to the incident beam, if f1 = 10 cm, f2 = 20 cm ? f1 f2 HRW A beam expander is made of two lenses as shown. What is the ratio of the intensities of the emergent beam to the incident beam, if f1 = 10 cm, f2 = 20 cm ? f1 f2 I f 2 1 f = 1 = I f 4 i ✓ 2 ◆ GR9677 38 GR9677 f 2 = 10 f1 f2 = 15 cm f1 + f2 = 16.5 cm f1 f2 38 The telescope Angular magnification The magnification relation is h0 i hi = h0 = h − o − o An object like the sun is very far away.
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