Angle of Refraction

When light enters a more optically dense medium, its speed is reduced. The angle of refraction is less than the angle of incidence. The refracted ray is said to be bent "toward the normal."

When light enters a less optically dense medium, its speed is increased. The angle of refraction is greater than the angle of incidence. The refracted ray is said to be bent "away from the normal."

The optical density of a medium determines the speed of light in that medium.

Index of refraction

Snell's law

A neat interactive applet demonstrating refraction and total internal reflection. Total Internal Reflection

A virtual refraction lab. Refraction Lab

Critical angle

Total internal reflection only occurs when a light ray passes from a more optically dense substance into a less optically dense substance. Total internal reflection is the principle behind fiber optics and binoculars.

Dispersion

Spectrum

Prism

Dispersion occurs because light of different wavelengths travel at different speeds through a medium. Red light has the longest wavelength and the highest velocity. Violet light has the shortest wavelength and the lowest velocity.

AP Multiple Choice Questions on Refraction & Snell's Law

1. Given a drawing depicting a ray incident upon a surface at an angle and its refracted ray, determine in which medium the speed of light is the greatest and in which medium the index of refraction is the greatest.
2. Use the optical density of a substance (or its index of refraction) to determine how wavelength, speed, and frequency change as a ray of light refracts when traveling from one medium to another.
3. Be able to determine from a drawing of refracted rays in various media the relationship between the indices of refraction (which is largest, smallest, the same, etc.).
4. Know prisms! Know which color of light is refracted the least and the most. Know how a spectrum produced by a prism would change if the medium is changed.
5. Be able to perform simple critical angle calculations.
6. Be able to determine the relationship between the two media's index of refraction when total internal reflection occurs.

AP Free Response Questions on Refraction

1. Use the index of refraction to calculate the speed of light in the medium. Use this speed and a given frequency to calculate wavelength.
2. Use Snell's law to calculate either the index of refraction of a medium or the angle of refraction.
3. Calculate the critical angle of a substance.
4. Know that a ray of light incident perpendicular to a surface does not refract, but passes through unchanged.
5. Calculate the angle of deviation for a ray passing out of a prism.
6. Be able to predict how the refraction changes when the incident (or refractive) medium is changed.

Lens

Lens Power

Types of lenses:

1. Convex lens (converging lens)
   • A convex lens is always thicker in the center than at the edges.
   • Light traveling through the lens goes slower through the thick center and faster through the thin ends causing the rays to focus or converge.
   • The focal length of a convex lens is always positive.
   • Real images are produced when the object is outside of the focus.
   • No image is produced when the object is at the focus.
   • Virtual images are produced when the object is within the focus.

   Move the lens and object in this applet to create your image. This applet is a hands-on way to see how the image distance and type of image change with changing object distance. A tutorial enables you to answer questions based upon the applet. Converging Lens

2. Concave lens (diverging lens)
   • A concave lens is always thinner in the middle than at the edges.
   • Light traveling through a concave lens goes faster through the center and slower through the ends. This causes the rays to diverge or not to focus.
   • The focal length of a concave lens is always negative.
   • Only virtual images are produced by a concave lens.

Move the lens and object in this applet to create your image. This applet is a hands-on way to see how the image distance and type of image change with changing object distance. A tutorial enables you to answer questions based upon the applet.Diverging Lens

Instructions for creating ray diagrams for lenses:

1. A ray passing through the optical center of the lens passes through unrefracted.
2. A ray incident upon the lens parallel to the principal axis passes through the focus; convex lenses use the focus on the opposite side of the lens and concave lenses use the focus on the same side of the lens.

An interactive applet in which you can see how images are created using ray diagrams for both convex and concave lenses. Ray Diagrams

Lens Equation

Focal Length

• f is positive for converging lenses (convex)
• f is negative for diverging lenses (concave)

Object Distance

• d_o is positive if the object is on the same side of the lens from which the light is incident
• d_ois negative if the object is on the opposite side of the lens from which the light is incident

Image Distance

• d_i is positive if the image is on the opposite side of the lens from which the light is incident; d_i is positive for a real image
• d_iis negative if the image is on the same side of the lens from which the light is incident; d_i is negative for a virtual image

• h_o is always positive

• h_i is positive if the image is upright
• h_iis negative if the image is inverted

When light passes through more than one lens, the image created by the first lens is located first. This image becomes the object for the second lens. If this image (the object for the second lens) and the first lens are on the same side of the second lens, the object distance is positive. If this image (the object for the second lens) and the first lens are on opposite sides of the second lens, the object distance is negative.

Locate the image created by the second lens. The total magnification is the product of the separate magnifications of each lens. Remember to follow the sign conventions above.

The focal length of a diverging lens can be found using combinations of lens. A converging lens with a smaller focal length than the diverging lens is placed in contact with the diverging lens. The image formed by the first lens becomes the object for the second lens. Since this object is on the opposite side of the lens than the incident light, it has a negative d_o. In other words, it is a virtual object.

Lensmaker's Equation

Optical Instruments

1. Camera - a camera contains a convex lens which focuses a real image on the film
2. Human eye - contains a convex lens which focuses an image on the retina
   • Nearsightedness (or myopia) occurs when the eye can only focus on close objects; it is usually caused by an eyeball which is too long
   • Farsightedness (or hyperopia) occurs when the eye can only focus on distance objects; it is usually caused by an eyeball which is too short
   • Abstigmatism is caused by an out-of-round cornea or lens
3. Magnifying glass - a converging lens with the object distance less than the focal length; a virtual, magnified image is produced
4. Telescope - Magnifies distant objects; the refracting telescope consists of two convex lenses. The focal length of the lens used as the eyepiece is small and that of the objective lens is large.
5. Compound Microscope - magnifies objects which are close. The focal length of the lens used as the eyepiece is large and that of the objective lens is small.

Spherical Aberration

Chromatic Aberration

AP Multiple Choice Questions on Lenses

1. Magnifying glass - know the type of lens it is, the type of image it produces, and the size of the image it produces relative to the object.
2. Be able to do simple calculations using the thin lens formula to predict if the image is virtual or real, upright or inverted, and/or on the opposite or same side of the lens as the object.
3. Use pictures of lenses to predict which is a converging lens.

AP Free Response Questions on Lenses

1. Be able to draw ray diagrams to locate an image using converging or diverging lenses.
2. Calculate the image location and size.
3. Predict whether the image is real or virtual and support your answer.
4. Draw ray diagrams for simple two-lens systems (convex/convex, convex/concave, and convex/spherical mirror).

Lenses Applet for AP

Converging Lenses Applet for AP

Diverging Lenses Applet for AP

Prism Applet for AP

Two Lenses or One Lens/One Mirror Applet for AP

Refraction & Lenses Sample Problems

Refraction Homework

Lenses Homework

AP Geometric Optics Objectives

AP Geometric Optics Class Problems