Physics 23: 6-10 Refraction and Lenses

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 6 to 10

Study Points

Section 6: Internal reflect occurs when light striking a surface between two transparent media is bent back into the first medium, rather than refracting through the surface into the second medium. The angle at which refraction through the surface turns into reflection is the critical angle: sin θ_c = n₂/n₁ sin 90° = n₂/n₁. Using media chose for their high internal reflection features allows us to create fiber optics or "light pipes" that send images around corners.
Section 7: Thin lenses can have surfaces that are concave, convex, or plane to the incoming light. The focal point distance (focal length) depends on the curvature of both sides of the lens.
Thin convex lenses are converging lenses that can focus light passing through them to a single point (the focal point). Light is bent as it enters the lens and again as it leaves the lens. Light rays pass through the focal point, so the image is considered a real image.
Thin concave lenses are diverging lenses that can spread light out. The focal point is the point where the diverging rays appear to meet when traced back through the lens. No actual light rays pass through this point, so the image is considered a virtual image.
Section 8: The focal length, image distances, and object distances for thin lenses are related by the thin lens equation: 1/d_p + 1/d_i = 1/f [Yes, this looks exactly like the Mirror equation!]. Magnification is also similar: m = h_i/h__o = -d_i/d_o. The sign of the magnification determines whether the image is inverted (negative) or upright (positive).
Section 9: When two lenses are combined, we determine the image location (d_i) from the first lens the light reaches, and use it as the object location (d_o) for the second lens.
Section 10: Lens makers craft lenses by polishing until the lens surface has a particular radius. By combining radii for the front and back sides of a lens, they can create lenses of different focal lengths: 1/4 = (n-1) (1/R₁ + 1/R₂). Note that the radius value is negative for concave lenses.

Key Equations

Relationship	Formula	Variables
Critical angle for Total Reflection	$\sin θ_{c} = \frac{n_{2}}{n_{1}}$	θ_c = angle at which light from the source is reflected parallel to the interface. n₁ = refraction index of first medium. n₂ = refraction index of medium beyond interface
Lens Power in diopters	$P = \frac{1}{f}$	f = focal length of lens
Thin lens equation (converging)	$\frac{1}{d_{0}} + \frac{1}{d_{i}} = \frac{1}{f}$	d_o = distance between object and lens d_i = distance between lens and image f = focal length of lens
Thin lens equation (diverging)	$\frac{1}{d_{0}} - \frac{1}{d_{i}} = - \frac{1}{f}$	d_o = distance between object and lens d_i = distance between lens and image f = focal length of lens
Magnification	$m = \frac{h_{i}}{h_{o}} = - \frac{d_{i}}{d_{o}}$	h_o = height of object h_i = height of image d_o = distance to object (positive if object and source are on same side of lens) d_i = distance to image (positive if image on opposite side of lens from source; positive for real image and negative for virtual image)
Lensmaker's Equation	$\frac{1}{f} = (n - 1) (\frac{1}{R_{1}} + \frac{1}{R_{2}})$	f = focal length n = index of refraction R₁ = radius of curvature of far side R₂ = radius of curvature of near side

Web Lecture

Read the following weblecture before chat: Lenses

Study Activity

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

From the tools, select Glasses > Ideal Lens and draw vertical straight line thin lens 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

Required: Complete the Mastery exercise with a passing score of 85% or better.
Go to the Moodle and take the quiz for this chat session to see how much you already know about astronomy!

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: Refraction Lab

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Physics

Chapter 23: 6-10 Assignment