Dr. Jie ZouPHY Chapter 35 The Nature of Light and the Laws of Geometric Optics

Dr. Jie ZouPHY Outline The ray approximation in geometric optics Reflection The law of reflection An application: Retroreflection Refraction Index of refraction Snell’s law of refraction

Dr. Jie ZouPHY The ray approximation in geometric optics Geometric optics: The study of the propagation of light. Ray approximation: In the ray approximation, we assume that a wave moving through a medium travels in a straight line in the direction of its rays.

Dr. Jie ZouPHY Reflection Reflection: When a light ray traveling in one medium encounters a boundary with another medium, part of the incident light is reflected. Specular reflection: Reflection of light from a smooth surface, where the reflected rays are all parallel to each other. Diffuse reflection: Reflection from any rough surface, where the reflected rays travel in random directions. In this book, we use the term reflection to mean specular reflection.

Dr. Jie ZouPHY The Law of reflection Law of reflection: The angle of reflection equals the angle of incidence:  1 ’ =  1. Some definitions: Normal: The normal is a line drawn perpendicular to the surface at the point where the incident ray strikes. Angle of reflection and incidence: Measured from the normal to the reflected and incident rays, respectively.

Dr. Jie ZouPHY Example 35.2: The double- reflected light ray Two mirrors make an angle of 120° with each other. A ray is incident on mirror M 1 at an angle of 65° to the normal. Find the direction of the ray after it is reflected from mirror M 2.

Dr. Jie ZouPHY Practical applications of reflection Retroreflection: If the angle between the two mirrors is 90°, the reflected beam will return to the source parallel to its original path.

Dr. Jie ZouPHY Refraction Refraction: When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray enters the second medium. The part that enters the second medium is bent at the boundary and is said to be refracted. sin  2 / sin  1 = v 2 / v 1  1 and  2 are the angle of incidence and angle of refraction, respectively. v 1 and v 2 are the speed of the light in the first and second medium, respectively. The path of a light ray through a refracting surface is reversible. All rays and the normal lie in the same plane.

Dr. Jie ZouPHY Index of Refraction and Snell’s Law of Refraction Index of refraction n of a medium: n  c/v c = 3 x 10 8 m/s: speed of light in vacuum. v: speed of light in the medium; v < c. n > 1 for any medium and n = 1 for vacuum (or approximately in air). Check Table 35.1 for different n values Snell’s law of refraction: n 1 sin  1 =n 2 sin  2 As light travels from one medium to another, its frequency does not change but its wavelength does. 1 n 1 = 2 n 2, or 1 / 2 = v 1 /v 2.

Dr. Jie ZouPHY Examples Problem #21: When the light illustrated in the figure passes through the glass block, it is shifted laterally by the distance d. Taking n = 1.50, find the value of d. Example 35.5: A laser in a compact disc player generates light that has a wavelength of 780 nm in air. (A) Find the speed of light once it enters the plastic of a compact disc (n = 1.55). (B) What is the wavelength of this light in the plastic?

Dr. Jie ZouPHY Quick Quiz If beam 1 is the incoming beam in the figure on the left, which of the other four red lines are reflected beams and which are refracted beams?

Dr. Jie ZouPHY Homework Ch 35, P. 1118, Problems: #6, 12, 22.