In Figure (a), a light ray in an underlying material is incident at angle 01 on a boundary with water, and some of the light refracts into the water. There are two choices of underlying material. For each, the angle of refraction 02 versus the incident angle 01 is given in Figure (b) below. The vertical axis scale is set by 01s =86°. Without calculation, determine whether the index of refraction of (a) material 1 and (b) material 2 is greater or less than the index of water (n = 1.33). What is the index of refraction of (c) material 1 and (d) material 2? 90° Water 45° (a) (b)
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- 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 timesThe 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?A beaker with a mirrored bottom is filled with a liquid whose index of refraction is nliq = 2.37. A light ray from air strikes the top surface of the liquid at an incident angle θin = 72.9° from the normal line to the liquid surface, as shown in the figure. What is the refraction angleθ1 of the light ray as it enters the liquid (in degrees; remember to use the scientific notation of numbers)?
- 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| 8₂0A ray of light travels from air into another medium, making an angle of θ1 = 45.0° with the normal A light ray in air is moving down and to the right and is incident on a second medium. It makes an angle θ1 with the vertical. Inside the vertical, it continues to move down and to the right but at a steeper slope than the incident ray. It makes an angle θ2 with the vertical. (a) Find the angle of refraction θ2 if the second medium is sodium chloride. °(b) Find the angle of refraction θ2 if the second medium is diamond. °(c) Find the angle of refraction θ2 if the second medium is benzene. °A beam of light traveling through air is incident up a transparent material at an angle of ??θi=70.43 degrees as shown in the image below. If the angle of the transmitted ray (??θt) as measured with respect to the direction normal to the surface of the material (dashed line in the image below) is 29.72 degrees, what is the index of refraction of of the material?
- The figure below shows the path of a beam of light through several layers with different indices of refraction. (Assume n 1.08.) n = 1,60 n = 1.40 n = 1.20 (a) If 0, = 20.0°, what is the angle 0, of the emerging beam? (b) What is the smallest incident angle 0, to have total internal reflection at the surface between the medium with n = 1.20 and the medium with n. = 1.08?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.(a) A small light fixture on the bottom of a swimming pool is 0.86 m below the surface. The light emerging from the still water forms a circle on the water surface. What is the diameter of this circle? (Give your answer, in m, to at least two decimal places.) m (b) What If? If a 1.58 cm thick layer of oil (noil 1.35) is spread uniformly over the surface of the water, what is the diameter of the circle of light emerging from the swimming pool? (Give your answer, in m, to at least two decimal places.) m =
- Consider a layer of Oil, Glass, and Air where the oil/glass boundary is parallel to the glass/air boundary. Let the index of refraction for the glass be 1.48 and the index of refraction for the oil to be 1.25. At what angle relative to the normal should a ray of light be directed upon the oil/glass interface such that it strikes the glass/air interface at the critical angle?The critical angle for total internal reflection at a liquid-air interface is 43.5°. If a ray of light traveling in the liquid has an angle of incidence of 30.0° at the interface with respect to the normal, what angle does the refracted ray in the air make with the normal? If a ray of light traveling in air has an angle of incidence of 30.0⚫ at the interface with respect to the normal, what angle does the refracted ray in the liquid make with the normal?In the figure, light is incident at angle 8₁ = 39° on a boundary between two transparent materials. Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air. If n₁ = 1.28, n₂ = 1.38, n3 = 1.34 and n4 = 1.45, what is the value of (a) 05 and (b) 04? 18₁ Air m n₂ 173 na