Goal To understand how mirrors and lenses work

Goal: To understand how mirrors and lenses work Objectives: 1) To understand how Plane mirrors create an image 2) To understand how Convex Mirrors reflect light 3) To understand the properties of Concave Mirrors 4) To be able to calculate the Focal Length and Magnification of a lens or mirror 5) To understand the similarities of Lenses and Mirrors

Plane mirrors • These are the sort of mirrors you find in a bathroom. • They are straight and flat.

Convex mirrors • Convex Mirrors curve away from you.

Concave Mirrors • Convex mirrors curve towards you

Some basic properties • Object distance. • This is denoted as p. • This is the physical distance the object is away from the mirror. • Radius of Curvature (C) is what the radius of a mirror would be if it was an entire sphere.

Image distance and focal length • This is the distance the image appears to be away from the mirror (denoted q). • Focal length (denoted f) is the distance from the mirror to the focal point (where all the light would come together for a light source very far away).

Mirror Equation • Finally some math… • 1/p + 1/q = 1/f • Yes, you can use that trick I showed you earlier with this! • So, f = pq / (p+q) • And p = -fq / (f – q) • The minuses due to 1/p = 1/f – 1/q

Sample • An object is place 5 cm away from a mirror which has a focal length of 2 cm. • What is the distance from the mirror to the image?

Sample • An object is place 5 cm away from a mirror which has a focal length of 2 cm. • What is the distance from the mirror to the image? • q = (on board) • Note that a negative means that the image is a virtual image (is in front of the mirror). • Positive values of q mean real image (behind the mirror). • p is always positive

Another • An object is 10 cm away from a mirror. • The image in the mirror is 5 cm behind the mirror. • A) is this a real or imaginary image? • B) what is the focal length of the mirror?

Magnification • m = h’ / h • That is it is the height of the image divided by the height of the actual object. • Also, m = -q / p • Note that when q is positive (real image) m is negative. • This means that the image is inverted (upside down). • What would be true about the image if q is negative?

Lenses • There are two types of lenses. • Diverging lenses make light spread out. • Diverging lenses tend to be concave. • Not that q and f are BOTH negative for a lens or mirror that is diverging. • Converging lenses make light focus on a point. • Converging lenses tend to be convex.

Diverging vs converging • Diverging (concave) lenses generate an image in front of the lens. • Is this a real or virtual image?

Diverging vs converging • Diverging (concave) lenses generate an image in front of the lens. • Is this a real or virtual image? • Virtual image • Since you have a virtual image, is q going to be positive or negative?

Diverging vs converging • Diverging (concave) lenses generate an image in front of the lens. • Is this a real or virtual image? • Virtual image • Since you have a virtual image, is q going to be positive or negative? • Negative! • Since q is negative will the magnification be positive or negative?

Diverging vs converging • Diverging (concave) lenses generate an image in front of the lens. • Is this a real or virtual image? • Virtual image • Since you have a virtual image, is q going to be positive or negative? • Negative! • Since q is negative will the magnification be positive or negative? • Positive (upright image)

Converging lens • q is usually, but not always positive. • This means the magnification will be negative (inverted image). • • However, q can be negative q = -fp / (f – p) So, if f is > p then q is actually negative. That is if the object is closer to the lens than the focal length you get a virtual image – otherwise you get a real image.

Conclusion • We learned about the different mirror and lens types. • We learned how to find object distance, image distance, and focal length. • We learned 2 ways to calculate magnification. • We learned the differences between real and virtual images and how they translate to inverted or upright images.