Show that if you have three polarizing filters, with the second at an angle of
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- Three polarizing sheets are placed together such that the transmission axis of the second sheet is oriented at 25.0° to the axis of the first, whereas the transmission axis of the third sheet is oriented at 40.0° (in the same sense) to the axis of the first. What fraction of an intensity of an incident unpolarized beam is transmitted by the combination?arrow_forwardTwo polarizing sheets P1 and P2 are placed together with their transmission axes oriented at an angle to each other. What is when only 25% of the maximum transmitted light intensity passes through them?arrow_forwardAn unpolarized beam of light is incident on a stack of ideal polarizing filters. The axis of the first filter is perpendicular to the axis of the last filter in the stack. Find the fraction by which the transmitted beams intensity is reduced in the three following cases. (a) Three filters are in the stack, each with its transmission axis at 45.0 relative to the preceding filter. (b) Four filters are in the stack, each with its transmission axis at 30.0 relative to the preceding filter. (c) Seven filters are in the stack, each with its transmission axis at 15.0 relative to the preceding filter. (d) Comment on comparing the answers to parts (a), (b), and (c).arrow_forward
- What angle is needed between the direction of polarized light and the axis of a polarizing filter to cut its intensity in half?arrow_forwardIf you have completely polarized light of intensity 150 W/m2 , what will its intensity be after passing through a polarizing filter with its axis at an 89.0 angle to the light’s polarization direction?arrow_forwardAt what angle is light inside crown glass completely polarized when reflected from water, as in a fish tank?arrow_forward
- Astronomers observe the chromosphere of the Sun with a filter that passes the red hydrogen spectral line of wavelength 656.3 nm, called the H line. The filter consists of a transparent dielectric of thickness d held between two partially aluminized glass plates. The filter is held at a constant temperature. (a) Find the minimum value of d that produces maximum transmission of perpendicular H light if the dielectric has an index of refraction of 1.378. (b) What If? If the temperature of the filter increases above the normal value, increasing its thickness, what happens to the transmitted wavelength? (c) The dielectric will also pass what near-visible wavelength? One of the glass plates is colored red to absorb this light.arrow_forwardThe index of refraction for water is about 43. What happens as a beam of light travels from air into water? (a) Its speed increases to 43c, and its frequency decreases. (b) Its speed decreases to 34c, and its wavelength decreases by a factor of 34. (c) Its speed decreases to 34c, and its wavelength increases by a factor of 43. (d) Its speed and frequency remain the same. (e) Its speed decreases to 34c, and its frequency increases.arrow_forwardA linearly polarized microwave of wavelength 1.50 cm is directed along the positive x axis. The electric field vector has a maximum value of 175 V/m and vibrates in the xy plane. Assuming the magnetic field component of the wave can be written in the form B = Bmax sin (kx t), give values for (a) Bmax, (b) k, and (c) . (d) Determine in which plane the magnetic field vector vibrates. (e) Calculate the average value of the Poynting vector for this wave. (f) If this wave were directed at normal incidence onto a perfectly reflecting sheet, what radiation pressure would it exert? (g) What acceleration would be imparted to a 500-g sheet (perfectly reflecting and at normal incidence) with dimensions of 1.00 m 0.750 m?arrow_forward
- (a) At what angle of incidence will the light reflected from water be completely polarized? (b) Does this angle depend on the wavelength of the light?arrow_forwardRefractive Index (n) is a ratio of the speed of light in a vacuum to the speed of light in materials such as glass, water, plastic, etc. Using Snell's Law, and given an air to glass interface with and angle of incidence of 15 degrees, what will be the angle of refractance R if the refractive index of the glass is 1.5 ? Snell's Law: n; (sin I) = n, (sin R) So, Sin R = n; (sin I) / n And, R = arcsin (n; (sin I) / n,) For each angle I, find angle R: 5. I=0, R = 6. I=45, R = 7. I= 60, R = 8. I = 75, R = = arcsin (1(.259)/1.5) = arcsin (.172) = 9.9 degrees Wavelength in Air- Light- Angle of Light -Wavelength in Glass Normal 90° R Air nj-1 Glassarrow_forwardUnpolarized light passes through two Polaroid sheets. The transmission axis of the analyzer makes an angle of 43.7° with the axis of the polarizer.(a) What fraction of the original unpolarized light is transmitted through the analyzer? (Enter your answer to at least three decimal places.) (b) What fraction of the original light is absorbed by the analyzer?arrow_forward
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