Section 3 Curved Mirrors Chapter 13 Section 3 Curved Mirrors

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 from spherical mirrors. Objectives

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 Curved Mirrors

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 Types of curved mirrors

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

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 spherical mirror

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

Concave mirrors

The Mirror Equation relates object distance (p), image distance (q), and focal length (f) of a spherical mirror. 1 𝑝 + 1 𝑞 = 1 𝑓 1 𝑜𝑏𝑗𝑒𝑐𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 + 1 image distance = 1 focal lenghth Mirror equation

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. 𝑀= ℎ ′ ℎ =− 𝑞 𝑝 𝑀= 𝑖𝑚𝑎𝑔𝑒 ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑏𝑗𝑒𝑐𝑡 ℎ𝑒𝑖𝑔ℎ𝑡 =− 𝑖𝑚𝑎𝑔𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑏𝑗𝑒𝑐𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑐𝑒 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 Magnification equation

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. Concave spherical mirrors

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. Examples with concave mirrors

Determine the sign and magnitude of the focal length and object size. f = +10.0 cm p = +30.0 cm The mirror is concave, so f is positive. The object is in front of the mirror, so p is positive. So using the mirror equation 1 𝑓 = 1 𝑝 + 1 𝑞 1 10 = 1 30 + 1 𝑞 Solve for q 1 10 − 1 30 = 1 𝑞 1 15 = 1 𝑞 q=15 cm solution

Magnification equation 𝑀=− 𝑞 𝑝 𝑀=−15/30 =-1/2=-.5 solution

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 mirror

Convex spherical mirrors Characteristic of convex mirror A convex mirror is part of the outer surface of a hollow sphere A convex mirror produces diverged rays A convex mirror does not form real images Convex mirror in daily life, used in cars, and used in stores to observe shoppers. Convex spherical mirrors

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. Convex mirror sample problem

solution Convex Mirrors Given: Unknown: Using mirror equation 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 solution 1 𝑓 = 1 𝑝 + 1 𝑞 1 −8 = 1 𝑝 + 1 −4.44 Solve for p 1 −8 − 1 −4.44 = 1 𝑞 1 10 = 1 𝑝 p=.1 cm

Using magnification equation M=-q/p M=.444 M=h’/h H=h’/m=5.63 cm solution

Forming an image in convex mirrors Three kinds of rays The ray parallel to the principal axis is reflected as if it is from focal point (f) The ray to focal point is reflected parallel to the principal axis The ray to the center of curvature C is reflected along its same path through C Forming an image in convex 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 a parabolic mirror. Parabolic mirrors

Spherical aberration and parabolic mirror

Student guided practice Do worksheet problems Student guided practice

Do problems 1-6 in your book page 462 homework

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