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- https://phys.libretexts.org/Courses/Skidmore_College/Introduction_to_General_Relativity/04%3A_Light_Orbits/4.01%3A_Impact_ParameterIn this chapter we will investigate the paths that photons take in Schwarzschild spacetime. That may seem like a silly question at first since it is often said that light travels in straight lines, bu...In this chapter we will investigate the paths that photons take in Schwarzschild spacetime. That may seem like a silly question at first since it is often said that light travels in straight lines, but remember that General Relativity messes with the rules of geometry, so photons can travel in what appears to us as a curved path.
- https://phys.libretexts.org/Bookshelves/Optics/Geometric_Optics_(Tatum)/01%3A_Reflection_and_Refraction/1.07%3A_The_RainbowRainbows are meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of mu...Rainbows are meteorological phenomenon that is caused by reflection, refraction and dispersion of light in water droplets resulting in a spectrum of light appearing in the sky. It takes the form of multicolored circular arcs. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun. Rainbows can be full circles, but observers normally see only an arc formed by illuminated droplets above the ground and centered on a line from the sun to the observer's eye.
- https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Graduate_Classical_Mechanics_(Fowler)/16%3A_Elastic_Scattering/16.03%3A_The_Differential_Cross_SectionThe differential cross section, written dσ/dΩ is the fraction of the total number of scattered particles that come out in the solid angle dΩ, so the rate of particle scatte...The differential cross section, written dσ/dΩ is the fraction of the total number of scattered particles that come out in the solid angle dΩ, so the rate of particle scattering to this detector is ndσ/dΩ, with n the beam intensity as defined above.
- https://phys.libretexts.org/Bookshelves/University_Physics/Radically_Modern_Introductory_Physics_Text_II_(Raymond)/13%3A_Newtons_Law_of_Gravitation/13.07%3A_Use_of_Conservation_Lawswhere m is the mass of the bullet, M is the mass of the moon, R is the radius of the moon, and v initial is the minimum initial velocity required for the bullet to escape. At apheli...where m is the mass of the bullet, M is the mass of the moon, R is the radius of the moon, and v initial is the minimum initial velocity required for the bullet to escape. At aphelion and perihelion, the radial part of the velocity of the asteroid is zero and the speed equals the tangential component of the velocity, v = v t . Thus, at aphelion and perihelion we can eliminate v in favor of the angular momentum:
