Chapter 34—Ray Optics Items covered in this chapter: Reflections Refraction Color Dispersion Thin Lenses New equations: n1sin1 = n2sin2 (Snell’s Law for refraction) (Thin Lens Equation)

Chapter 34—Ray Optics The ray (or particle) model of light. Light rays travel in straight lines with a speed of v = c/n. Light rays can cross. A light ray travels forever unless it interacts with matter. A light ray then reflects and/or refracts. Within a material light can be either scattered or absorbed. An object is a source of light rays (even if it’s not). The eye sees by focusing a diverging bundle of rays.

Reflection Some definitions: Normal Line Angle of Incidence i Angle of Reflection r i r For reflection r = i 5

Reflection Irregular or Diffuse Reflection Vs. Regular or Specular Generally, one gets diffuse reflection when irregularities in the reflecting surface are larger than the wavelength of visible light Mt. Washington 6

More definitions: Si So i = image distance o = object distance

Sample Reflection Problem You have a height of h. What is the shortest mirror on the wall in which you can see your full image? Also: where must the top of the mirror be hung?

n1 n2 Refraction 1 Index of Refraction c = speed of light in a vacuum v = speed of light in the material in question 2 n2

It turns out that the index of refraction of a substance is slightly different depending upon the frequency of light passing through a substance.

Refraction 1 2 From experience, we know that when light travels from one medium to another, it’s path is bent. For example, we know that water “bends light”. 7

Refraction n1sin1=n2sin2 And we get Snell’s Law Where v1 is the velocity of light in medium1 and v2 is the velocity of light in medium2. Now, the speed of light in a vacuum is 3*108 m/s. We don’t like dealing with such large numbers, so we give materials numbers in a range we can deal with… And we get Snell’s Law n1sin1=n2sin2 1 2 We define the Index of Refraction as: n = 8

Let’s take a look a closer look at Snell’s Law. n1sin1=n2sin2 Let’s try shining a light from the bottom of a swimming pool, up toward the surface. In this case, n1=1.33 and n2=1.00 Thus, we have that sin2=1.33sin1 n2=1.00 n1=1.33 http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=66 9

Thin Lens: A lens is considered thin when its thickness is small compared to all the other distances involved. Two types of thin lenses: Convex and Concave f f o i http://www.phys.hawaii.edu/~teb/optics/java/clens/

Spherical Mirrors (Concave): Ray Tracing Method: Ray 1: This ray is initially parallel to the principal axis. It passes through the focal point F after reflection from the mirror. Ray 2: This ray passes through the focal point F and is reflected back parallel to the principal axis. Ray 3: This ray travels along a line that passes through the center of curvature C and follows a radius of the spherical mirror. (i.e. it reflects back on itself)

Spherical Mirrors (Concave): Mirror Equations:

Focal length f is + for a concave mirror f is – for a convex mirror Object distance o is + if the object is in front of the mirror (real) o is – if the object is behind the mirror (virtual) Image distance i is + if image is in front of the mirror (real) i is – if image is behind the mirror (virtual) Magnification m is + if image is upright m is – if image is inverted

f f o i http://www.phys.hawaii.edu/~teb/optics/java/clens/

0) We look at the light rays coming from the top of the object. Ray 1 goes parallel to the axis of symmetry until you get to the middle of the lens. At the middle of the lens, you then draw a straight line that goes through the opposite focal point of the lens. Ray 2 goes straight through the middle of the lens and is not distorted. Ray 3 goes through the near focus, until it gets to the middle of the lens. From the middle of the lens, the ray continues in a direction parallel to the axis of symmetry.

Formation of a virtual image through a converging lens.

The Thin Lens Equation: f f s s’

Note what happens when the object is far away:

For a telescope, due to diffraction, the best angular resolution that can be seen by the telescope is:

Topics in Chp 34 that will be in the exam: Remembered that the index of refraction is defined n = c/v Snell’s Law: n1sin1 = n2sin2 Ray Tracing Converging and Diverging Lenses We used the Thin-Lens Equation to calculate the position of the image and the magnification. Maybe you’ll need to be able to use the “spherical lens equation” or “lens maker equation”.