Chapter 13 Section 3 Curved Mirrors

Objectives

Calculate distances and focal lengths using the mirror equation for concave and convex spherical mirrors.

Draw ray diagrams to find the image distance and magnification for concave and convex spherical mirrors.

Distinguish between real and virtual images.

Describe how parabolic mirrors differ fromspherical mirrors.

Curved Mirrors

Curved mirrors are like plane mirrors they too have smooth, shiny surfaces that reflect

light. The surface can either curve in (concave) or out

(convex) as shown below

Types of curved mirrors

Thus far in this unit, our focus has been the reflection of light off flat surfaces and the formation of images by plane mirrors. In Lessons 3 and 4 we will turn our attention to the topic curved mirrors, and specifically curved mirrors that have a spherical shape. Such mirrors are called spherical mirrors. The two types of spherical mirrors are shown in the diagram on the right. Spherical mirrors can be thought of as a portion of a sphere that was sliced away and then silvered on one of the sides to form a reflecting surface

Concave spherical mirror

A concave spherical mirror is a mirror whose reflecting surface is a segment of the inside of a sphere.

Concave mirrors can be used to form real images.

A real image is an image formed when rays of light actually pass through a point on the image. Real images can be projected onto a screen.

Concave spherical mirror

Concave spherical mirror

Rays from very distant things are nearly parallel to each other

a concave mirror brings parallel rays to a focus at a point called the principal focus (F)

the distance from the mirror to the principal focus is called the focal length

highly curved mirror have short focal lengths

Concave mirrors

If a concave mirror were thought of as being a slice of a sphere, then there would be a line passing through the center of the sphere and attaching to the mirror in the exact center of the mirror. This line is known as the principal axis. The point in the center of the sphere from which the mirror was sliced is known as the center of curvature and is denoted by the letter C in the diagram below. The point on the mirror's surface where the principal axis meets the mirror is known as the vertex and is denoted by the letter A in the diagram below. The vertex is the geometric center of the mirror. Midway between the vertex and the center of curvature is a point known as the focal point; the focal point is denoted by the letter F in the diagram below. The distance from the vertex to the center of curvature is known as the radius of curvature (represented by R). The radius of curvature is the radius of the sphere from which the mirror was cut. Finally, the distance from the mirror to the focal point is known as the focal length (represented by f). Since the focal point is the midpoint of the line segment adjoining the vertex and the center of curvature, the focal length would be one-half the radius of curvature.

Concave mirrors

Mirror equation

The Mirror Equation relates object distance (p), image distance (q), and focal length (f) of a spherical mirror.

Magnification equation

Unlike flat mirrors, curved mirrors forms images that are not the same size as the object. The measure of how large or small the image is with respect to the original object’s size is called the magnification of the image.

For an image in front of the mirror, m is negative and the image is upside down, or inverted When the image is behind the mirror, M is positive and the image is upright with respect to the object

Concave spherical mirrors

Ray diagrams can be used for checking values calculated from the mirror and magnification equations for concave spherical mirrors.

Concave mirrors can produce both real and virtual images.

Examples with concave mirrors

A concave spherical mirror has a focal length of 10.0 cm. Locate the image of a pencil that is placed upright 30.0 cm from the mirror. Find the magnification of the image. Draw a ray diagram to confirm your answer.

solution

1. Determine the sign and magnitude of the focal length and object size.f = +10.0 cm p = +30.0 cmThe mirror is concave, so f is positive. The object is in front of the mirror, so p is positive.

So using the mirror equation

Solve for q

q=15 cm

solutionMagnification equation

15/30 =-1/2=-.5

Convex spherical mirror

A convex spherical mirror is a mirror whose reflecting surface is outward-curved segment of a sphere.

Light rays diverge upon reflection from a convex mirror, forming a virtual image that is always smaller than the object.

Convex spherical mirrors

Characteristic of convex mirror

1.A convex mirror is part of the outer surface of a hollow sphere

2.A convex mirror produces diverged rays

3.A convex mirror does not form real images

4.Convex mirror in daily life, used in cars, and used in stores to observe shoppers.

Image formation by a convex mirror

Convex mirror sample problem

An upright pencil is placed in front of a convex spherical mirror with a focal length of 8.00 cm. An erect image 2.50 cm tall is formed 4.44 cm behind the mirror. Find the position of the object, the magnification of the image, and the height of the pencil.

solution

Convex MirrorsGiven:

Because the mirror is convex, the focal length is negative. The image is behind the mirror, so q is also negative.f = –8.00 cm q = –4.44 cm h’ = 2.50 cm

Unknown:p = ? h = ?

Using mirror equation Solve for p

p=.1 cm

solutionUsing magnification equationM=-q/pM=.444M=h’/hH=h’/m=5.63 cm

Forming an image in convex mirrors

Three kinds of rays1.The ray parallel to the principal axis is reflected as if

it is from focal point (f)2.The ray to focal point is reflected parallel to the

principal axis3.The ray to the center of curvature C is reflected along

its same path through C

Parabolic mirrors

Images created by spherical mirrors suffer from spherical aberration.

Spherical aberration occurs when parallel rays far from the principal axis converge away from the mirrors focal point.

Parabolic mirrors eliminate spherical aberration. All parallel rays converge at the focal point of aparabolic mirror.

Spherical aberration and parabolic mirror

Student guided practice

Do worksheet problems

homework Do problems 1-6 in your book page 462

Closure Today we learned about concave and convex mirrors Next class we are going to learn about color and

polarization