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 Problem No 8 Below are five images which were obtained as follows. Laser beam has been directed to a sheet of white paper (in one case, to a white wall with a rough surface). The emerging bright spot of the laser beam has been photographed with a digital camera; the lens axis was kept approximately perpendicular to the sheet of paper. The camera has been focused to infinity (not to the bright spot!); so, the sensor surface coincided with the focal plane of the camera lens. The images were taken with a lens of focal length $F=300$ mm; the diameter of the lens was $D=75$ mm (for one image, the effective diameter of the lens was reduced by a diaphragm down to 38 $\pm 4$ mm). Each image is a square crop from the image recorded by the sensor; the scaling factor of these images can be calculated from the fact the pixel length on the sensor was $9.6\;\mu$m; the respective length of each image is also indicated in millimeters. Note that the distance from the camera to the bright spot was not kept strictly constant between the experiments; the distance variations were within ca 10%. (a) Using these images, estimate the size of the bright spot created by the red laser. (So, inaccuracies within a factor of 2 are acceptable.) Note that the bright spot was slightly elliptical and approximately of the same size for all the three lasers used. (b) Explain why the image of the bright spot created by the violet laser on a sheet of white paper is qualitatively different from all the other images. Image recorded by the sensor of a digital camera when a bright spot was created on a sheet of white paper (laser printer paper, A4) by a red laser beam ($\lambda=670$ nm) . The size of this square image crop on the sensor was 7.5 mm.   Same as above, except that the diameter of the camera lens was reduced by a diaphragm. The square size on the sensor was 4.7 mm.   Same as the first figure, except that a green laser ($\lambda =532$ nm) has been used. The square size on the sensor was 7.5 mm.   Same as above, except that a violet laser ($\lambda =404$ nm) has been used. The square size on the sensor was 7.4 mm.   Same as above, except that instead of a white laser printer paper, a white wall with a rough surface has been used (the white wall surface height fluctuations were around 0.2 mm). The square size on the sensor was 6.7 mm.

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