# Refraction

Student Learning Objectives
Lessons / Lecture Notes
Important Equations
Example Problems
Applets and Animations

Student Learning Objectives

• To understand the ray model and how it applies to refraction.
• To understand and apply Snell's law.
• To calculate the critical angle for total internal reflection.
• To apply ray tracing for both concave and convex lenses.
• To understand images and image formation.
• To use the thin-lens and magnification equations to analyze image formation by lenses.

Lessons / Lecture Notes

The Physics Classroom (conceptual)

PY106 Notes from Boston University (algebra-based):

Introductory physics notes from University of Winnipeg (algebra-based):

HyperPhysics (calculus-based)

PHY2049 notes from Florida Atlantic University (calculus-based):

PHY2044 notes from Florida Atlantic University (calculus-based)

General Physics II notes from ETSU (calculus-based)

Important Equations

Example Problems

Problem 1
Light in vacuum is incident on the surface of a glass slab. In the vacuum the beam makes an angle 32.0o with the normal to the surface, while in the glass it makes an angle of 21.0o with the normal. What is the speed of light in the glass? (Solutions)

Problem 2
Two converging lenses (f1 = 9.00 cm and f= 6.00 cm) are separated by 18.0 cm.  The lens on the left has the longer focal length.  In object stands 12.0 cm to the left of the left-hand lens in the combination.  (a) Locate the final image relative to the lens on the right.  (b) Obtain the overall magnification.  (c) Is the final image real or virtual?  With respect to the original object, is the final image (d) upright or inverted and is it (e) larger or smaller? (Solutions)

Applets and Animations
 Huygen's Principle Reflection/Refration This applet is a sort of tutorial which explains the reflection and the refraction of waves by the principle of Huygens. Explanations of each of the steps are provided in the text box. Reflection and Refraction Illustrating reflection and refraction, including total internal reflection. Refraction of Light A ray of light coming from the top left strikes the boundary surface of two media. The applet shows the reflected and the refracted ray and calculates the corresponding angles. Refraction Explanation This animation shows wave fronts entering a mediums at a non-zero angle of incidence. Refraction through a Prism This applet shows the refraction of light through a prism. The user can control the index of refraction of the prism as well as the position and shape of the prism. Image Formation of a Converging Lens This applets shows the image formation by a converging lens. The three principle rays are shown. Geometric Optics How does a lens form an image? See how light rays are refracted by a lens. Watch how the image changes when you adjust the focal length of the lens, move the object, move the lens, or move the screen. Thick Lens The Thick Lens model allows the user to simulate a lens (mirror) by adjusting the physical properties of a transparent (reflecting) object and observing the object's effect on a beam of light.  The user can adjust the concavity of the sides, the index of refraction and its environment, and the height and width of the object as well as the size of the incident light and the horizontal position of the transparent object.