Please help me solve all of these problems. They are a sample exam for my class but my professor wont give us the solutions. Document Preview: Biophotonics Homework Question #1 (10%): An optical imaging system consists of two positive lenses (L1 and L2). L1 has a focal length f1 = 10 cm, and L2 has a focal length f2 = 5 cm. Two lenses are separated by L = 40 cm. An object (denoted by the vertical arrow) with height h is located in front of the first lens with a distance of 15 cm. (a) In the following diagram, draw the final image formed by these two lenses. (5%) (b) Using the lens equation, please calculate the location of the final image with respect to the center of L2. Also what is the final magnification? (5%) Question #2 (10%): A dual-wavelength spectrometer uses 780 nm and 830 nm. The molar extinction coefficients for oxy-hemoglobin (HbO2) and deoxy-hemoglobin (Hb) at these two wavelengths are: ( HbO2 780nm = 710 cm-1M-1, ( Hb 780nm = 1075 cm-1M-1, ( HbO2 830nm = 974 cm-1M-1, ( Hb 830nm = 693 cm-1M-1. The spectrometer measures absorption coefficients at these two wavelengths are: (a 780nm = 0.057 cm-1, (a 830nm = 0.063 cm-1, please calculate the concentration for HbO2 and Hb (in unit of (M), as well as total hemoglobin concentration, and oxygen saturation. Question #3 (10%): Randomly polarized light (such as sun light) with intensity of I0 passes through three polarizers (P1, P2, P3) consecutively. P1 and P3 are stationary, and their polarization planes are perpendicular to each other. In contrary, the polarization plane of P2 is rotating at an angular frequency of (0. Assume the polarization plane of P2 is parallel to that of P1 at t=0. Please calculate the final intensity I3(t). Question #4 (10%): A horizontal ray hitting a prism with n=1.5, tip angle a=4o. The ray will be deflected by an angle d=(n-1)a. The ray is further reflected by a vertical mirror. Now, if I want to make the final ray becomes horizontal again, how many degree (and in what direction) should I turn the mirror? Question Attachments: Homework7prob.doc; Please help me solve all of these problems. They are a sample exam for my class but my professor wont give us the solutions. Document Preview: Biophotonics Homework Question #1 (10%): An optical imaging system consists of two positive lenses (L1 and L2). L1 has a focal length f1 = 10 cm, and L2 has a focal length f2 = 5 cm. Two lenses are separated by L = 40 cm. An object (denoted by the vertical arrow) with height h is located in front of the first lens with a distance of 15 cm. (a) In the following diagram, draw the final image formed by these two lenses. (5%) (b) Using the lens equation, please calculate the location of the final image with respect to the center of L2. Also what is the final magnification? (5%) Question #2 (10%): A dual-wavelength spectrometer uses 780 nm and 830 nm. The molar extinction coefficients for oxy-hemoglobin (HbO2) and deoxy-hemoglobin (Hb) at these two wavelengths are: ( HbO2 780nm = 710 cm-1M-1, ( Hb 780nm = 1075 cm-1M-1, ( HbO2 830nm = 974 cm-1M-1, ( Hb 830nm = 693 cm-1M-1. The spectrometer measures absorption coefficients at these two wavelengths are: (a 780nm = 0.057 cm-1, (a 830nm = 0.063 cm-1, please calculate the concentration for HbO2 and Hb (in unit of (M), as well as total hemoglobin concentration, and oxygen saturation. Question #3 (10%): Randomly polarized light (such as sun light) with intensity of I0 passes through three polarizers (P1, P2, P3) consecutively. P1 and P3 are stationary, and their polarization planes are perpendicular to each other. In contrary, the polarization plane of P2 is rotating at an angular frequency of (0. Assume the polarization plane of P2 is parallel to that of P1 at t=0. Please calculate the final intensity I3(t). Question #4 (10%): A horizontal ray hitting a prism with n=1.5, tip angle a=4o. The ray will be deflected by an angle d=(n-1)a. The ray is further reflected by a vertical mirror. Now, if I want to make the final ray becomes horizontal again, how many degree (and in what direction) should I turn the mirror? Question Attachments: Homework7prob.doc
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