sin(0. – 0'b) d = t- cos 0' n n' n P
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Light is incident in air at an angle θa (as in fig) on the upper surface of a transparent plate, the surfaces of the plate being plane and parallel to each other. (a) Prove that θa = θ′ a. (b) Show that this is true for any number of different parallel plates. (c) Prove that the lateral displacement d of the emergent beam is given by the relationship d as attached, where t is the thickness of the plate. (d) A ray of light is incident at an angle of 66.0° on one surface of a glass plate 2.40 cm thick with an index of refraction of 1.80. The medium on either side of the plate is air. Find the lateral displacement between the incident and emergent rays.
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- 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 searchLight propagates from air to oil (refracti0on oil n oil =1.49) with an angle of 36° with the surface of oil. The light propagates through oil/water (refraction index n water = 1.33). What is the angle of this light ray when it enters? (a) the oil, and then (b) the water? (c) What would be the refracted angle if the ray entered the water directly? (d) What would be the speed of the light in oil and water? Oil Air Water 36°An electromagnetic plane wave has an electric field given by: E(x, t) = - m)j[cos (kx – (12.65x1012rad/s)t] (3.10x105V/ %3D
- 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.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| 8₂0(a) The index of refraction for violet light in silica flint glass is 1.66, and that for red light is 1.62. What is the angular spread (in degrees) of visible light passing through a prism of apex angle 60.0° if the angle of incidence is 45.0°? See figure below. Visible light O Angular spread 0 Deviation of red light B V Screen R (b) What If? What is the angular spread (in degrees) of visible light passing through a prism of apex angle 60.0° if the angle of incidence is 90°?
- A ray of light crosses the boundary between some substance with n = 1.54 and air, going from the substance into air. If the angle of incidence is 29◦ what is the angle of refraction? Calculate to 1decimal.Laser light is passed through a angle of incidence in air of 0₁ rod made out of a material with an index of refraction of 1.63, a length L = 45.0 cm, and square cross section of length h = 3.00 mm on a side as shown in the figure. If the light enters at the center of the rod with an 47.5°, determine the number of total internal reflections before it emerges from the opposite end of the rod. 42.0 cm T 3.10 mmA ray of light is incident on an air/water interface. The ray makes an angle of θ1 = 29 degrees with respect to the normal of the surface. The index of the air is n1 = 1 while water is n2 = 1.33. Write an expression for the reflection angle ψ, with respect to the surface.