06 – Concave or Converging Mirrors PW2 - Reflection 06 – Concave or Converging Mirrors

Remember the Diagram & Components of Concave Mirrors

Image Characteristics for Concave Mirrors There are five (5) different situations, depending on where the object is located

Image Characteristics for Concave Mirrors 1) Object is located BEYOND “C” Image will be located between C and F Image is inverted Upside down Magnification is less than 1.0 Image is smaller than the object Image is real Light rays converge at the image location You could place a sheet of paper at the image location and view the image on the paper

Image Characteristics for Concave Mirrors 2) Object is located at “C” Image will also be located at “C” Image is inverted Upside down Magnification is 1.0 Image is same size as object Image is real Light rays converge at the image location You could place a sheet of paper at the image location and view the image on the paper

Image Characteristics for Concave Mirrors 3) Object is located between “C” and “F” Image located beyond C Image is inverted Upside down Magnification is greater than 1.0 Image is larger than the object Image is real Light rays converge at the image location You could place a sheet of paper at the image location and view the image on the paper

Image Characteristics for Concave Mirrors 4) Object is located at “F” No image is formed After reflecting the light rays are travelling parallel to each other and will not produce an image

Image Characteristics for Concave Mirrors 5) Object is located in front of “F” Image is located somewhere on the opposite side of the mirror (inside the mirror) Image is erect Right side up Magnification is greater than 1.0 Image is larger than the object Image is virtual Light rays do not actually converge on the location Any attempt to project the image on a sheet of paper would not be possible since light does not pass through the location

Locating Images using Math A ray diagram helps determine the approximate location and size of the image.   To obtain numerical information, we can use the Mirror equation and the Magnification equation.

The Mirror Equation Where: The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f). Where: do: is the distance from the object to the mirror (vertex) di: is the distance from the image to the mirror f: is the focal length (½c)

The Magnification Equation The Magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho). Since M = hi/ho or (-)di/do, the negative sign is necessary so that we get a negative (-) value indicating the image is inverted Remember, we often have inverted images with converging mirrors.

SIGN CONVENTIONS: f is + if the mirror is a concave mirror (converging) f is - if the mirror is a convex mirror (diverging) di is + if the image is a real image and located on the object's side of the mirror. di is - if the image is a virtual image and located behind the mirror. hi is + if the image is an upright image (and therefore, also virtual) hi is - if the image an inverted image (and therefore, also real)

Examples 1) An object 5.0 cm tall is placed 22.0 cm in front of a converging mirror with a radius of curvature of 30.6 cm. Determine the image distance and the image size. Known info: do = 22.0cm Radius = 30.6 so f = ½ R  15.3cm

Examples 2) The same object as before is placed in front of the same mirror, this time at a distance of 8.2 cm from the mirror. Determine the image distance and the image size.

Extra Examples 3)An object is located 30.0 cm from a converging mirror with a focal length of 5.0 cm. a) Where will the image be formed? Known information: f = 5.0 cm do = 30.0 cm

Extra Examples b) What is the magnification? The image is smaller and inverted - negative sign.

Extra Examples c) If the object is 4.0 cm tall, how tall is the image? The image is inverted because hi is negative.