# HW1 - n water = 1 33 What is the new Brewsters angle 3...

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ECE 455: Optical Electronics Homework 1 Due: Sept. 6, 2011 1 Photon Energy, Frequency, and Wavelength There are many ways to specify the energy and wavelength of a photon. In practice, they are often used interchangeably, and it is important to be able to convert to and from all forms. The following chart contains a number of coherent light sources and their respective photon wavelengths or energies. Complete the chart. Source E (eV) λ (nm) λ ( ˚ A) ν (Hz) ν (cm - 1 ) DVD Laser Diode 1.907 Ar + 454.6 He:Ne 6328 Nd:YAG 2 . 817 × 10 14 KrF 5.00 CH 3 OH (THz Laser) 84.154 2 Brewster’s Angle Quartz windows at Brewster’s angle are commonly used for gas lasers, like the He:Ne laser, in the manner shown in Figure 1. 1. At what angle, θ , should the glass slab be placed with respect to the cavity axis such that the Brewster’s angle condition is satisﬁed? Assume that n air = 1 . 0 and n quartz = 1 . 5. Figure 1: Glass slab at Brewster’s angle 1

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2. Now assume that the window is submerged in water (
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Unformatted text preview: n water = 1 . 33). What is the new Brewsters angle? 3 Propagation Matrices and Ray Tracing 1. Derive the ray matrix for the plane dielectric interface (see Figure 2). Figure 2: A planar dielectric interface 2. Derive the ray matrix for the plane dielectric slab of thickness d (see Figure 3). Figure 3: A planar dielectric slab 3. A ray initially parallel to the optical axis propagates in air through a series of optical elements as shown in Figure 4. What is the distance d 3 at which the ray crosses the optical axis in the slab? Assume that r 1 = 0 . 2 cm, d 1 = 18 cm, and d 2 = 0 . 5 cm. Also assume that the lenses are perfect spherical elements with f 1 =-50 cm and f 2 = 35 cm, that n air = 1 . 0, and that n slab = 2 . 4. 2 Figure 4: An arbitrary optical setup for ray tracing 3...
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HW1 - n water = 1 33 What is the new Brewsters angle 3...

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