Images in Concave Mirrors

Properties  The mirror has a reflecting surface that curves inward.  When you look at objects in the mirror, the image appears distorted.

Ray Diagram  You can apply the same rules of reflection for a plane mirror by thinking of the curved surface as many small, flat mirrors. Small, flat mirrors

 If you draw the normal for each of the small mirrors, they will all meet at one point called the centre of curvature (C) of the mirror. Centre of curvature

 The thick, horizontal normal that touches the centre of the mirror is called the principal axis. It helps you locate the positions of objects that are in front of the mirror. The point at which the principal axis cuts the mirror is called the vertex (V). C Principal axis vertex

 If an incident ray passes through the centre of curvature, the angle of reflection will be zero since it passes over the normal and reflects back on itself. C

 When the incident ray is put parallel to the principal axis, it intersects the principal axis at a point called the focal point (F).  The focal length is the distance between the vertex of a mirror and the focal point.  When the incident ray is put parallel to the principal axis, it intersects the principal axis at a point called the focal point (F).  The focal length is the distance between the vertex of a mirror and the focal point. Focal point Rays parallel to principal axis Focal length

 When drawing a ray diagram to predict the position of an image, it is helpful to draw the object so that the bottom is on the principal axis.  This means that the bottom of the image will be on the principal axis too.  Use the laws of reflection to draw 2 incident rays.  Trace back the reflected rays to locate the image point for the top of the object.  When drawing a ray diagram to predict the position of an image, it is helpful to draw the object so that the bottom is on the principal axis.  This means that the bottom of the image will be on the principal axis too.  Use the laws of reflection to draw 2 incident rays.  Trace back the reflected rays to locate the image point for the top of the object.

Steps…  The first ray put through the top of the object, parallel to the principal axis (it will pass through the focal point)  Second ray: through top of object and through focal point, it should be parallel to principal axis.  Third ray: drawn through the centre point to the top of the object (should reflect back on itself)  The first ray put through the top of the object, parallel to the principal axis (it will pass through the focal point)  Second ray: through top of object and through focal point, it should be parallel to principal axis.  Third ray: drawn through the centre point to the top of the object (should reflect back on itself)

You try it!!  Follow 10.2 and draw a ray diagram for an object that is between the focal point and the mirror. List the characteristics of the image.  Follow 10.3 and draw a ray diagram for an object that is between the centre of curvature and the focal point. List the characteristics of the image  Follow 10.4 and draw a ray diagram for an object that is behind the centre of curvature and the focal point. List the characteristics of the image  Follow 10.2 and draw a ray diagram for an object that is between the focal point and the mirror. List the characteristics of the image.  Follow 10.3 and draw a ray diagram for an object that is between the centre of curvature and the focal point. List the characteristics of the image  Follow 10.4 and draw a ray diagram for an object that is behind the centre of curvature and the focal point. List the characteristics of the image

Mirror and Magnification Equations  You can predict the characteristics of an image using 2 equations: the mirror equation and the magnification equation.  Mirror equation: allows you to calculate the location of the image. 1 = f d i d o  Magnification: tells you the size/height of the image relative to the object. m = h i = -d i h o d o  You can predict the characteristics of an image using 2 equations: the mirror equation and the magnification equation.  Mirror equation: allows you to calculate the location of the image. 1 = f d i d o  Magnification: tells you the size/height of the image relative to the object. m = h i = -d i h o d o

Example:  Problem: A concave mirror has a focal length of 12cm. An object with a height of 2.5cm is placed 40.0cm in front of the mirror. Calculate the distance and height.  A) mirror equation: 1 = f d i d o (rearrange the formula) 1 = d i f d o (substitute) 1 = d i 12cm 40.0cm (solve) d i = 17.14cm  Problem: A concave mirror has a focal length of 12cm. An object with a height of 2.5cm is placed 40.0cm in front of the mirror. Calculate the distance and height.  A) mirror equation: 1 = f d i d o (rearrange the formula) 1 = d i f d o (substitute) 1 = d i 12cm 40.0cm (solve) d i = 17.14cm

 The image is 17cm from the mirror. It is a positive number, so it will be in front of the mirror.  B) Magnification: m = h i = -d i h o d o __ h i__ = cm 40.0 h i = -1.07cm The height is 1.1cm. The image height is negative, so the image is inverted.  The image is 17cm from the mirror. It is a positive number, so it will be in front of the mirror.  B) Magnification: m = h i = -d i h o d o __ h i__ = cm 40.0 h i = -1.07cm The height is 1.1cm. The image height is negative, so the image is inverted.

You Try It!!!  P. 427 # 1-5  P. 430 # 3-8  P. 427 # 1-5  P. 430 # 3-8