Lenses Converging Lens Diverging Lens F F f f

Web Link: Spherical mirrors and lenses Find the focal length of a converging lens by holding it up to a window. (See how far away from the lens you need to hold a piece of paper to focus the image on the paper.) Web Link: Spherical mirrors and lenses

Light passes through a lens Ray Tracing for Lenses Light passes through a lens There is a focal point on both sides of a lens Converging Lens: Ray #1: Parallel to the axis Refracts through F Ray #2: Through F Refracts parallel to axis Ray #3: Through Center of lens undeflected

Example: Camera

Example: Slide Projector

Example: Magnifying Glass Web Link: Ray tracing

Object distance > 2f: Image is real, smaller, and inverted Results: Ray Tracing for Converging Lenses (in each case, draw in the 3 rays for practice) Object distance > 2f: Image is real, smaller, and inverted F 2F Object between f and 2f: Image is real, larger, inverted F 2F Object between f and mirror: Image virtual, larger, upright F 2F

Now, for Diverging lenses…… Web Link: Spherical mirrors and lenses For a Diverging Lens: Ray #1: Parallel to the axis on the left Refracts as if it came from F on the left Ray #2: Heads toward F on the right Refracts parallel to the axis on the right Ray #3: Through the center of the lens undeflected

Example: Glasses to correct nearsightedness 2 Example: Glasses to correct nearsightedness

Web Link: Ray Tracing Summary for Mirrors and Lenses Results: Ray Tracing for Diverging Lenses (draw in the 3 rays for practice) No matter where the object is: Image is always virtual, smaller and upright F Web Link: Ray tracing Web Link: Ray Tracing Summary for Mirrors and Lenses

These equations also work on lenses: The Thin Lens Equation The Magnification Equation But the variables are defined slightly differently now because………. For a lens, a real image is on the opposite side as the object For a mirror, a real image was on the same side as the object

Sign conventions for Lenses Focal length (f) + converging - diverging Object distance (do) + object on the left Image distance (di) + image on the right (real) - image on the left (virtual) Magnification (m) + upright - inverted

Ex: lens 13cm book If the image of the book is 5.0 cm below the lens, find the focal length of the lens.

Ex: A camera with a focal length of 50 mm takes a photograph of a 100 m tall building from 350 m away. How tall is the image on the film?

Far Point – Farthest distance the eye can focus on (should be  ) The Human Eye Web Links: Eye lens, Vision and Eyesight Near Point – Closest distance the eye can focus on (about 25 cm when we are young) Far Point – Farthest distance the eye can focus on (should be  )

Nearsightedness can be corrected with diverging lenses Someone who is Nearsighted cannot focus on far away objects. (Their far point is not at infinity.) Nearsightedness can be corrected with diverging lenses Here’s how it works

Ex:                                Without my contact lenses, I need to stand 35 cm or less from the TV in order to see it in focus. Find the focal length of the contact lenses that correct my vision.

Someone who is Farsighted cannot focus on objects too near. Farsightedness can be corrected with converging lenses Here’s how it works

Ex: The man has a near point of 48 cm. His reading glasses are 2.0 cm from his eyes, and with them on, he can read the newspaper as close as 25 cm to his eyes. Find the focal length of his glasses

Can you think of two ways that this problem could be eliminated? Lens Aberrations 1) Spherical Aberration Can you think of two ways that this problem could be eliminated?

2) Chromatic Aberration How to correct this problem? Compound (Achromatic) Lens