The numerical aperture (NA) of a fiber characterizes the ability of a fiber to collect light (a high NA means it collects more light). The NA is defined as the sine of the maximum external angle of a ray entering the fiber that can be trapped by total internal 1/2 reflection. Show that NA = n, sine, =(n° – n²)"
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- 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| 8₂0The 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 white light traveling through air enters a block of glass that has an index of refraction of 1.44 for the red end of the spectrum and 1.46 for the violet end. If the ray has an angle of incidence of 60.0 degrees with respect to the normal of the interface boundary, what's the angular separation between the red and violet ends of the spectrum within the glass?
- 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 light beam containing red and violet wavelengths is incident on a slab of quartz at an angle of incidence of 44.20°. The index of refraction of quartz is 1.455 at 660 nm (red light), and its index of refraction is 1.468 at 410 nm (violet light). Find the dispersion of the slab, which is defined as the difference in the angles of refraction for the two wavelengths.A light beam containing red and violet wavelengths is incident on a slab of quartz at an angle of incidence of 56. The index of refraction of quartz is 1.455 at 660 nm (red light), and its index of refraction is 1.468 at 410 nm (violet light). Find the dispersion of the slab, which is defined as the difference in the angles of refraction for the two wavelengths. 1.31º 1.05º 0.35º 0.50º
- 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 white light traveling through air enters a triangular prism that has an index of refraction of 1.511 for the red end of the spectrum and 1.537 for the violet end and an apex angle of 64.8 degrees. If the ray has an angle of incidence of 46.3 degrees with respect to the normal of the interface boundary, what is the angular separation between the red and violet ends of the spectrum upon exiting the prism? Measure this in degrees to 2 decimal places.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?