Different isotopes of the same element emit light at slightly different wavelengths. A wavelength in the emission spectrum of a hydrogen atom is 656.45 nm; for deuterium, the corresponding wavelength is 656.27 nm. (a) What minimum number of slits is required to resolve these two wavelengths in second order? (b) If the grating has 500.00 slits/mm, find the angles and angular separation of these two wavelengths in the second order
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Different isotopes of the same element emit light at slightly different wavelengths. A wavelength in the emission spectrum of a hydrogen atom is 656.45 nm; for deuterium, the corresponding wavelength is 656.27 nm. (a) What minimum number of slits is required to resolve these two wavelengths in second order? (b) If the grating has 500.00 slits/mm, find the angles and angular separation of these two wavelengths in the second order
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- A beam splitter is an optical device that splits a beam of light - half of the incident light is transmitted through the beam splitter, and half is reflected. Supposed we could make a beam splitter that reflects only 35% and transmits the other 65% (rather than 50/50). A beam of laser light with wavelength 656 nm is incident on our imaginary 35/65 beam splitter, at an angle of 45°. The beam pulse lasts 1.50 ms, and has a diameter of 0.60 mm. The intensity of the transmitted beam is 3.25 kW/m2. Draw a clear physics diagram of the problem. What is the energy of a photon from this laser? Find the peak Electric field of the reflected beam. Find the peak Magnetic field of the incident beam. What color is the laser beam? What momentum is transferred to the beam splitter by the laser pulse?You are underwater, on the seafloor, looking up. Use n=1.33 for the index of refraction of water. At what range of angles, as measured above the seafloor, can you NOT see out of the water? (You will need a carefully labeled diagram showing just where the light is coming from, and a reasoned explanation of why your answer is correct.)A laser beam is normally incident on a diffraction grating. The wavelength of the incident light is 1 = 560 nm, and the third-order maximum of the diffraction pattern is measured to be at an angle of 32.0°. (a) What is the density of rulings for the grating (in grooves/cm)? grooves/cm (b) Determine the total number of primary maxima that can be observed in this situation. primary maxima Need Help? Read It
- The resolution of the eye is ultimately limited by the pupil diameter. What is the smallest diameter spot the eye can produce on the retina if the pupil diameter is 2.41 mm? Assume light with a wavelength of λ = 550 nm. (Note: The distance from the pupil to the retina is 25.4 mm. In addition, the space between the pupil and the retina is filled with a fluid whose index of refraction is n = 1.336.)Hint: The size of the spot is twice the distance from the main axis to the first minimum.O 23.8° A bichromatic source produces light having wavelengths in vacuum of 450 nm and 650 nm. The indices of refraction are 1.440 and 1.420, respectively. In one situation, a ray of the bichromatic light, in air, is incident upon the oil at an angle of incidence of 50.0°. The angle of dispersion between the two refracted rays in the oil is closest to which measure? O0.7° O 0.5° O 0.9° O 1.3° O1.1° nere to searchA layer of oil, with a refractive index of 1.40798, exactly 1 mm thick, floats on water. Light of vacuum wavelength 632.800 nm, emitted by a stabilized He-Ne laser, is reflected at normal incidence by the oil. Question 1 1 pts The index of refraction of the oil varies slightly with the vacuum wavelength of the light. Find this altered wavelength in nm: Question 2 1 pts How many wavelengths are contained in the light wave passing back and forth through the oil? (Hint: the reflected wave is shifted by X/2.) Please enter your answer as a whole number. Question 3 1 pts Does the light reflected from the two surfaces of the oil interfere constructively or destructively? Destructively O Constructively
- Light with a wavelength in vacuum of 530 nm falls perpendicularly on a biological specimen that is 1.10 ?m thick. The light splits into two beams polarized at right angles, for which the indices of refraction are n1 = 1.320 and n2 = 1.333, respectively. (a) Calculate the wavelength of each component of the light while it is traversing the specimen. (Give your answers to at least one decimal place.) ?n1 = answer in nm ?n2 = answer in nm (b) Calculate the phase difference between the two beams when they emerge from the specimen. answer in degrees °The resolution of the eye is ultimately limited by the pupil diameter. What is the smallest diameter spot the eye can produce on the retina if the pupil diameter is 2.62 mm? Assume light with a wavelength of λ = 550 nm. (Note: The distance from the pupil to the retina is 25.4 mm. In addition, the space between the pupil and the retina is filled with a fluid whose index of refraction is n = 1.336.)Hint: The size of the spot is twice the distance from the main axis to the first minimum.Light from glowing hydrogen contains many discrete spectral lines, of which two are Ha (hydrogen-alpha) and HB (hydrogen-beta), with wavelengths of 656.3 nm and 486.1 nm, respectively. Find the first- order angular separation between these wavelengths in a spectrometer that uses a grating with 6000 slits per cm.
- Astronomers observe the chromosphere of the Sun with a filter that passes the red hydrogen spectral line of wavelength 656.3 nm, called the Holine. The filter consists of a transparent dielectric of thickness d held between two partially aluminized glass plates. The filter is kept at a constant temperature. (a) Find the minimum value of d that will produce maximum transmission of perpendicular H light if the dielectric has an index of refraction of 1.400. (Enter your answer to one decimal place.) nm (b) If the temperature of the filter increases above the normal value increasing its thickness, what happens to the transmitted wavelength? (Assume the index of refraction of the dielectric remains constant.) ---Select--- (c) The dielectric will also pass what near-visible wavelength? One of the glass plates is colored red to absorb this light. nmThe Hubble Space Telescope (HST) orbits Earth at an altitude of 613 km. It has an objective mirror that is 2.40 m in diameter. If the HST were to look down on Earth's surface (rather than up at the stars), what is the minimum separation of two objects that could be resolved using 549 nm light? [IVote: The HST is used only for astronomical work, but a (classified) number of similar telescopes are in orbit for spy purposes.]Young's experiment uses a laser with a wavelength λ = 632.8 nm, a slit separation of 0.5 mm and an observation distance of 40 cm. What is the separation of the stripes if the experiment is performed in (a) air (n = 1,0003), (b) a carbon dioxide environment (n = 1,0005), and (c) in water (n = 1,333)?