Physics 23: 1-5 Light Rays and Reflection

Homework

Reading Preparation
Key Equations
WebLecture
Study Activity
Chat Preparation Activities
Chapter Quiz
Lab Work

Reading Preparation

Text Reading: Giancoli, Physics - Principles with Applications, Chapter 23: Sections 1 to 5

Study Points

REFLECTION

Section 1: In the ray model, we assume light travels in straight lines unless reflected by a mirror or refracted by a change in media. This principle underlies the geometric optics of the Greeks and Arabs.
Section 2: The law of reflection states that for a plane mirror, the angle of incidence (to the normal of the mirror) must equal the angle of reflection. The image appears to be on the far side of the mirror.
Section 3: A spherical mirror can be concave (reflecting surface is on the inside curve, rays bent so that they converge) or convex (reflecting surface is on the outside of the curve, and rays are bent so that they diverge). In a convex mirror, the principal axis is the normal line intersecting the center of the curve.
- Rays parallel to the principal axis will be bent back to a point on the axis, called the focal point for that ray. The location of the focal point for a given ray depends on the distance from the point where the ray strikes the mirror to the intersection of the principle axis.
- The distance from the focal point to where the principal axis intersects with the mirror is the focal length f of the mirror.
- Spherical aberration is the spread of light rays to slightly different focal points. It is greater for rays that strike the rims (far from the center) of mirrors with tight curvature (r is small).
- The distance from the object being reflected (often the source of light) is the object distance.
- For spherical mirrors, the image distance, object, distance, and focal length are related by the formula 1/d_o + 1/d_i = 1/f
- Magnification is the ratio of the image height to the object height, and is related to image and object distances: M = h_i/h_o = d_i/d_o. Notice that the bigger the difference between d_i and d_o, the bigger the magnification.
REFRACTION
Section 4: When light passes from one medium to another, it changes speed. This causes the wave to bend. The ratio of the speed in the medium compared to the speed of light in a vacuum is the index of refraction n = v/c. The greater v is, the smaller c is.
Section 5: In refraction, the angle of incidence is related to the angle of refraction n₁ sin θ₁ = n₂ sin θ₂.

Key Equations

Relationship	Formula	Variables
Plane Mirror Reflection	$θ_{incidence} = θ_{reflection}$	θ_i = angle between incident ray and normal to the surface θ_r = angle between reflected ray and normal to the surface
Approximate focal length of spherical mirror	$f = \frac{r}{2}$	f = focal length (distance along primary axis between mirror and focal point r = radius of sphere
Mirror equation	$\frac{1}{d_{0}} = \frac{1}{d_{i}} + \frac{1}{f}$	1/d_{o = distance along primary axis between object and mirror 1/d_i = distance along primary axis between image and mirror}
Index of refraction	$n = \frac{v}{c}$	n = index (varies by material in medium) v = velocity of light in medium c = speed of light in a vacuum
Snell's law	$n_{1} \sin θ_{1} = n_{2} \sin θ_{2}$	n₁ = index of refraction in first medium θ₁ = angle of incident ray to normal to the surface n₂ = index of refraction in second medium θ₂ = angle of refracted ray in the new medium to normal at the surface

Web Lecture

Read the following weblecture before chat: The Optics of Refraction and Reflection

Study Activity

Use the simulator Ray Optics Site to play with concepts of reflection.

From the tools, select Mirrors > Segment and draw a vertical mirror in the middle of the screen.
Select a point source and place it to the left of the mirror.
What happens to beams that intersect with the mirror as you move the point source towards and away from the mirror?
What happens to beams that miss the mirror or are directed away from the mirror?
Select Extended Rays, which creates the path of the bent rays. Where is the focal point?
Use reset to clear the screen and start a new experiment.
Continue experimenting with mirrors of different shapes. What happens to the rays reflected from a circular curve if the source is above the axis of curvature? Closer to the mirror than the radius of curvature? Further than the focal point?

Chat Preparation Activities

Forum question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

Chapter Quiz

The chapter quiz is not yet due.

Lab Work

If you want lab credit for this course, you must complete at least 18 labs; you may complete more if you are preparing for the AP exam.. One or more lab exercises are posted for each chapter as part of the homework assignment. We will be reviewing lab work at regular intervals, so do not get behind!

Lab Instructions: Reflection Lab

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Physics

Chapter 23: 1-5 Assignment