You are working in an optical research laboratory. One of the pieces of experimental apparatus involves a beam of light entering a transparent rod (see the figure below) of diameter d = 1.50 um and index of refraction n = 1.24, surrounded by air. Your supervisor has given you the task of determining the cone of acceptance for the rod, which is the maximum angle 0may (in degrees) for which the light rays incident on the end of the rod are subject to total internal reflection along the walls of the rod.
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- A beam of light moves through a slab of glass as shown in the figure. The index of refraction of the glass is ng = 1.5. The index of refraction of air is na = 1. The incident angle of the light is \theta i = 44\deg . Part (a) If the refraction angle of the light at the upper surface of the slab is \theta 1, express sin\theta 1 in terms of \theta i, na, and ng. Part (b) The incident angle of the light on the lower surface of the slab is \theta 2. What is the relation between \theta 1 and \theta 2? Part (c) The refraction angle of the light on the lower surface of the slab is \theta f. Express sin(\theta f) in terms of \theta 2, na, and ng.A light ray travelling in medium a is refracted into medium b. The angle of incidence is 50.5° and the angle or refraction is 60.8°. Both angles are measured from the normal to the interface. What is the ratio of the index of refraction of medium a to that of medium b?A light beam reflects off two parallel reflecting surfaces that are = 202 cm long and separated by a distance of s = 65.0 cm. If the beam of light enters this region as shown, with the angle 0 = 25.1°, determine the following. Ꮎ (a) the number of times the light beam reflects off the left surface Have you redrawn the figure with all angles and distances labeled? How is the entrance angle related to the angle of Incidence and the angle of reflection for the mirrors? times (b) the number of times the light beam reflects off the right surface times
- The figure below shows the path of a beam of light through several layers with different indices of refraction. (Assume n = 1.02.) e₁ n = 1.60 02 n = 1.40 n = 1.20 MA (a) If ₁ = 28.0°, what is the angle 2 of the emerging beam? o 1 (b) What is the smallest incident angle ₁ to have total internal reflection at the surface between the medium with n = 1.20 and the medium with Па = 1.02?F: (a) In figure below, a beam of monochromatic light reflects and refracts at point A on the interface between material 1 with index of refraction n₁ = 1.77 and material 2 with index of refraction n₂ = 1.33. The incident beam makes an angle of 50° with the interface. What is the angle of reflection at point A? What is the angle of refraction there? (b) What is the angle of reflection at point B? What is the angle of refraction there? 50° e, ie A 18 721 Tho no ng Air A| 8₂0In the figure, a light ray in air is incident on a flat layer of material 2 that has an index of refraction n₂ = 2.7. Beneath material 2 is material 3 with an index of refraction n3. The ray is incident on the air-material 2 interface at the Brewster angle for that interface. The ray of light refracted into material 3 happens to be incident on the material 2-material 3 interface at the Brewster angle for that interface. What is the value of n3? Number Units 09₂ Air ng ng
- A ray of light strikes a flat block of glass at an incidence angle of ?1 = 38.6°. The glass is 2.00 cm thick and has an index of refraction that equals ng = 1.52. (a) What is the angle of refraction, ?2,that describes the light ray after it enters the glass from above? (Enter your answer in degrees to at least 2 decimal places.) b.)With what angle of incidence, ?3,does the ray approach the interface at the bottom of the glass? (Enter your answer in degrees to at least 2 decimal places.)Three sheets of plastic have unknown indices of refraction.Sheet 1 is placed on top of sheet 2, and a laser beam is directed unto the sheets from above so that it strikes the interface at an angle of 26.5 degrees with the normal. The refracted beam in sheet 2 makes an angle of 31.7 degrees with the normal. The experiment is repeated with sheet 3 on top of sheet 2, and with the same angle of incidence, the refracted beam makes an angle of 36.7 degrees with the normal. If the experiment is repeated again with sheet 1 on top of sheet 3, determine the expected angle of refraction in sheet 3?. Assume the same angle of incidence.ray of light strikes a flat block of glass at an incidence angle of ?1 = 38.6°. The glass is 2.00 cm thick and has an index of refraction that equals ng = 1.52. a.)What is the angle of refraction, ?2, that describes the light ray after it enters the glass from above? (Enter your answer in degrees to at least 2 decimal places.) b.) With what angle of incidence, ?3, does the ray approach the interface at the bottom of the glass? (Enter your answer in degrees to at least 2 decimal places.) c.) With what angle of refraction, ?4, does the ray emerge from the bottom of the glass? (Enter your answer in degrees to at least 1 decimal place.) d.) The distance d separates the twice-bent ray from the path it would have taken without the glass in the way. What is this distance (in cm)? e.) At what speed (in m/s) does the light travel within the glass? f.) How many nanoseconds does the light take to pass through the glass along the angled path shown here?