Mirrors Reflection of Light

Mirrors Word bank MIRROR Any regular reflecting surface that can produce an image of an object standing in front of it Common mirrors are made of flat glass painted with silver on one side.

Mirrors CHARACTERISTICS OF MIRROR IMAGES A) IMAGE SIZE Images formed by mirrors can be enlarged, reduced or of the same size as the object forming the image. Image formed by a plane mirror is of the same size as the object

Mirrors IMAGE SIZE The apparent reduction in the size of an image as an object moves farther away from the mirror can be explained by the diagram below: object Actual image: same size as the object; same distance from the mirror as the object image in the mirror as seen by the person (There’s an apparent reduction in size!)

Mirrors CHARACTERISTICS OF MIRROR IMAGES B) ORIENTATION Images formed by mirrors can either be oriented upright or inverted. Image formed by a plane mirror is always upright.

Mirrors CHARACTERISTICS OF MIRROR IMAGES C) NATURE Images formed by mirrors can either be real (formed in front of the mirror) or virtual (formed at the back of the mirror). Word bank VIRTUAL IMAGE Image formed by light rays that do not converge at the location of the image

Mirrors Word bank SPHERICAL MIRROR Mirror formed from sections of a sphere Also called a curved mirror There are two types: the convex mirror and the concave mirror

Mirrors Word bank CONCAVE MIRROR Mirror that curves inward or toward its center Converges parallel rays of light to a single point called the FOCAL POINT

Mirrors Word bank CONVEX MIRROR Mirror that curves outward or away from its center Diverges parallel rays of light creating an image behind the mirror

Mirrors FEATURES OF THE SPHERICAL MIRROR Spherical mirror R Principal axis C F f C – Center of the sphere R – Radius of curvature: Distance between C the mirror F – Focal point: Point halfway between C and the mirror f – Focal length: Distance between F and the mirror; Equal to ½ R

Mirrors RAY TRACING METHOD Method used to describe the location, nature, size and orientation of image formed by a spherical mirror

Mirrors FORMATION OF IMAGE USING RAY-TRACING METHOD This process requires tracing of any two rays suggested below: 1) An incident ray from the tip of the object drawn parallel to the principal axis will pass through the focal point upon reflection

Mirrors FORMATION OF IMAGE USING RAY-TRACING METHOD 2) An incident ray connecting the tip of the object and the focal point will be reflected parallel to the principal axis 3) An incident ray connecting the tip of the object and the center will be reflected back along the same line

Mirrors The intersection of the reflected rays will form the tip of the image C F Principal axis Ray 3 object Ray 2 Ray 1

Mirrors C F Principal axis Ray 3 object Ray 2 incident ray Ray 1 reflected ray

Mirrors Ray 1 For convex mirrors, the focal point and the center are located at the back of the mirror. You have to project the reflected rays back (into the mirror) to locate the intersection. Ray 3 Ray 2 Principal axis object F C incident rays reflected rays back projections

SEATWORK An object is placed at different positions in front of a concave mirror. Describe the image formed at each position by completing the table. Location of object Location of image Nature Orientation Size Between the mirror and the focal point F At the focal point F Between the center C and the focal point F At the center C Beyond the center C

Mirrors MIRROR EQUATION Another way of locating the images formed by spherical mirrors is by the use of the mirror equation: focal length, f: distance from the focal point to the mirror object distance, do: distance from the object to the mirror image distance, di: distance from the image to the mirror magnification, m: the number of times the image is larger than the object height of object, ho height of image, hi

Mirrors SIGN CONVENTIONS Focal length can be either positive or negative Focal length is positive for concave mirrors and negative for convex mirrors Image distance can be either positive or negative Image distance is positive if the image is real and negative if the image is virtual Object distance can only be positive Magnification can be either positive or negative Magnification is positive if the image is upright and negative if the image is inverted If the magnitude of the magnification is: Less than 1, image is reduced Equal to 1, image is of the same size as the object Greater than 1, image is enlarged

EXAMPLE An object is 4.00 cm from a concave mirror with a focal length of 10.0 cm. Find the location, size, orientation and nature of the image formed. Given: do= 4.00 cm f = 10.0 cm di= ? m = ?

= -6.67 cm (Image is located 6.67 cm from the mirror) m = -di/do SOLUTION di = (dof)/(do- f) = (4.00 cm x 10.0 cm)/(4.00 cm-10.0 cm) = -6.67 cm (Image is located 6.67 cm from the mirror) m = -di/do = -(-6.67 cm)/(4.00 cm) = 1.67 (Image is 1.67x larger than the object) The image is virtual (di is negative), upright (m is positive) and enlarged (magnitude of m is greater than 1)

EXAMPLE 2 A girl stares at a shiny Christmas ball with a diameter of 60.0 cm. If her face is 20.0 cm from the ball, describe the location, size, orientation and nature of her image. The ball is a convex mirror because the center is located inside the ball. Therefore, f is negative. F is half the radius (which is half the diameter). do= 20.0 cm f = -15.0 cm di= ? m = ?

= (20.0 cm x -15.0 cm)/(20.0 cm-(-15.0 cm)) SOLUTION di = (dof)/(do- f) = (20.0 cm x -15.0 cm)/(20.0 cm-(-15.0 cm)) = -8.57 cm (Image is located 8.57 cm from the ball) m = -di/do = -(-8.57 cm)/(20.0 cm) = 0.43 (Image size is 0.43x size of the object) The image is virtual (di is negative), upright (m is positive) and reduced (magnitude of m is less than 1)

HOMEWORK 1) A shaving mirror of focal length 25.0 cm is used by your dad while he shaves 12.0 cm in front of it. How much does the mirror magnify your dad’s face? 2) A convex mirror of focal length 9.0 cm creates an image whose distance is 9.0 cm. Describe the image formed if the object’s height is 5.0 cm.