* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Final Exam
Photon scanning microscopy wikipedia , lookup
Confocal microscopy wikipedia , lookup
Gamma spectroscopy wikipedia , lookup
Silicon photonics wikipedia , lookup
Dispersion staining wikipedia , lookup
Diffraction topography wikipedia , lookup
Optical flat wikipedia , lookup
Thomas Young (scientist) wikipedia , lookup
Phase-contrast X-ray imaging wikipedia , lookup
Ellipsometry wikipedia , lookup
Nonimaging optics wikipedia , lookup
Optical tweezers wikipedia , lookup
Surface plasmon resonance microscopy wikipedia , lookup
Rutherford backscattering spectrometry wikipedia , lookup
Ultrafast laser spectroscopy wikipedia , lookup
Optical aberration wikipedia , lookup
Atmospheric optics wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Anti-reflective coating wikipedia , lookup
Optical coherence tomography wikipedia , lookup
Harold Hopkins (physicist) wikipedia , lookup
Retroreflector wikipedia , lookup
Interferometry wikipedia , lookup
Magnetic circular dichroism wikipedia , lookup
Nonlinear optics wikipedia , lookup
Diffraction wikipedia , lookup
Astronomical spectroscopy wikipedia , lookup
NAME: Exam 3 – PHYS 355 - OPTICS Mendes, Fall 2008, Dec 15, 2008 Start time: 8:00 a.m., End time: 10:30 am Open textbook, notes, homeworks, and quizzes Calculators allowed; no other electronic device allowed Where it is appropriate, make sure to provide physical units to your numerical answer 1/7 (10 points) 1) Sunlight is incident on an optical filter that transmits light with a center wavelength of 500 nm and a bandwidth of 1.2 nm. Determine the frequency bandwidth and the coherence length of the transmitted light. 2/7 (10 points) 2) Here’s a way to measure the optical wavelength of a light beam by measuring a physical distance: Monochromatic light illuminates a Michelson interferometer. One of its mirrors (mirror 1 in Figure below) is moved by 25 µm, and it is observed that 89 fringe-pairs, bright and dark, pass by the detector during this process. Determine the wavelength of the light beam. Mirror 2 Beam Splitter Mirror 1 Light source Detector 25 µm 3/7 (30 points) 3) A He-Cd laser (442 nm) is incident on a screen containing two very narrow horizontal slits separated by 180 µm. A fringe pattern appears on a screen held 1.2 m away. a) What is the distance from the central axis to the first zero of the light intensity? b) How far in mm from the central axis is the fourth bright fringe? c) Now consider that a 1-mm glass slide (n = 1.52) is inserted behind the top slit. How much will the fringe pattern move along the y-axis? Is it going to move up or down? y 442 nm 180 µm 1.2 m 4/7 (10 points) 4) An electromagnetic plane wave is incident on an opaque screen that contains a single and long horizontal slit that is 20 cm wide in the vertical direction. As shown in the Figure below, a detector, far away from the screen, but moving parallel to it, locates the first minimum of light intensity at an angle of 34° above the central axis. What are the wavelength and frequency of this electromagnetic radiation? detector 20 cm 34° 5/7 (20 points) 5) Consider that the lenses in the human eyes form an imaging system where optical aberrations are almost negligible. The pupil diameter in human eyes is typically around 2 mm under bright illumination. Under those conditions: a) What is the smallest angular width that is possible to resolve with the human eyes? For this calculation, consider the optical wavelength that our eyes are most sensitive (green, 550 nm) b) From the angular width calculated above, determine the smallest details we can expect to resolve for an object located at 25 cm in front of our eyes, which is typically the closest distance that our eyes can still accommodate. State your answer in micrometers, µm. Make sure your answer is reasonable to you: don’t tell me that you can see a hydrogen atom or that the smallest object you can resolve is a tennis ball. 6/7 (20 points) 6) White light plane waves are incident normally (in other words, the angle of incidence is 0°, or more precisely, the angle between the incident k-vector and the normal to the sample surface is 0°) on a transmission diffraction grating. If the diffraction grating has 1 cm : 2,000 lines per cm, we then know that the period of the grating is a = 2, 000 a) At what angle from the central axis will green light (550 nm) emerge in the first-order spectrum (m = 1)? b) Consider that 4,000 grating lines (N = 4,000) are used to disperse the incident light beam (for example, either the light beam width or the grating region is limited to 2-cm wide, whichever is the smallest). At about 550 nm, what is the angular width, Δθ , of the first-order spectrum (m =1)? c) What is the dispersion, dθ , of the first-order spectrum (m = 1) at about 550 nm? dλ d) Under the conditions considered above, what is the smallest wavelength range, Δλ , one can expect to resolve (to separate) at the first-order spectrum (m = 1) around the 550nm wavelength? a 7/7