Reflection from Flat Surfaces Do not copy this slide into your notes. Reflection from Flat Surfaces Image Object The image formed is a Virtual Image. i.e. the image is located at a place where any viewer perceives the light as coming from but is not at a place where the light rays either emanate from or go to. http://class.phys.psu.edu/hopkins/javaapplets.htm

Parabolic curved mirrors Principal axis

HowStuffWorks Videos "Elements of Physics: Light and Optics" HowStuffWorks Videos "Light, Lenses and Lasers: Curved Mirrors"

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Add these to your diagram Focal Point Concave Mirror Object Centre of Curvature Principal Axis

Ray Tracing C=centre of curvature. Let’s develop a rule for each ray: C-Ray: Incident rays passing through the C reflect back through C. P-Ray: Incident rays parallel to the principal axis reflect back through the focal point. F-Ray: Incident rays that pass through the focal point before striking the mirror reflect from the mirror parallel to the principal axis. C=centre of curvature. A concave mirror has a real focus at: f

Ray Diagram for an object between the centre of curvature (2f which is C) and the primary focus (1f).

Ray Diagram for an object between the centre of curvature (2f) and the primary focus (1f). Rule 1: Rays parallel to the principal axis reflect through the focal point.

Ray Diagram for an object between the centre of curvature (2f) and the primary focus (1f). Rule 2: Rays passing through the principal focal point reflect from the concave mirror parallel to the principal axis.

Ray Diagram for an object between the centre of curvature (2f) and the primary focus (1f). Rule 3: An image is formed where the rays cross. This lets you find the distance from the mirror to the image, di

Ray Diagram for an object between the centre of curvature (2f) and the primary focus (1f). Rule 4: Rays passing through the centre of curvature that go through the top of the object will also...

Ray Diagram for an object between the centre of curvature (2f) and the primary focus (1f). … go through the top of the image.

Ray Diagram for an object between the centre of curvature (2f) and the primary focus (1f). Rule 5: Rays that strike exactly at the vertex of the mirror reflect so that the incident angle equals the reflected angle.

Ray Diagram for an object between the centre of curvature (2f) and the primary focus (1f). Notice the pattern?

Let’s do another one, but this time, place the object between the focal point and the mirror

Ray Diagram for an object between the mirror and the primary focus (1f).

Rule 1: Virtual Rays passing through the focal point reflect from the concave mirror parallel to the principal axis. Ray Diagram for an object between the mirror and the primary focus (1f).

Rule 3: Rays passing through the centre of curvature… Ray Diagram for an object between the mirror and the primary focus (1f).

… reflects back through the centre of curvature and produce a virtual ray that continues straight through the mirror. Ray Diagram for an object between the mirror and the primary focus (1f).

Rule 4: An image is formed where the rays cross Rule 4: An image is formed where the rays cross. This lets you find the distance from the mirror to the image, di Ray Diagram for an object between the mirror and the primary focus (1f).

Ray Diagram for an object between the mirror and the primary focus (1f).

Rule 5: Rays that are incident on the mirror parallel to the principal axis will reflect through the focus. Notice the virtual ray that is produced. Ray Diagram for an object between the mirror and the primary focus (1f).

Rule 6: Rays that strike exactly at the vertex of the mirror reflect so that the incident angle equals the reflected angle. Ray Diagram for an object between the mirror and the primary focus (1f).

Let’s see that again.

Try this one!

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Quick - Let’s describe the S-A-L-T of these images!

Sample Ray Optics Problems f f

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Part 2: Calculations in Curved Mirrors

Reflection from Curved Surfaces do hi ho di A real image is formed. Rays of light actually go where the image is found. In the diagram, based on the path of the green ray: ho/ hi = do/ di Based upon the path of the orange ray : ho/ hi = (do - f)/f do/ di = (do - f)/f or Equation 1 1/f = 1/do + 1/di Magnification is given by Equation 2: m = hi/ ho = - di/do where the minus sign indicates an inverted image

SIGN CONVENTIONS >1, larger +Upright + Real <1, smaller   Magnification, M Height of Image, hi Position of Image, di >1, larger +Upright + Real <1, smaller - Inverted - Virtual

Example 1 An object is place 60 cm in front of a concave mirror with a focal length of 24 cm . Describe the image. 1/f = 1/do + 1/di 1/24 = 1/60 + 1/di 10/240 = 4/240 + 1/di 1/di = 6/240 di = 40 m = -di/do = -40/60 = - .67 Object is real, smaller, and inverted hi ho di 60

Example 2 An object is place 12 cm in front of a concave mirror with a focal length of 24 cm Describe the image. 1/f = 1/do + 1/di 1/24 = 1/12 + 1/di di = -24 (neg sign indicates virtual image) m = -di/do = - 24/24 = -1 Object is larger, upright, located behind mirror, virtual hi ho di

Part C: Convex Lenses (Diverging Lenses) Write this section on your own lined paper.

Let’s develop a rule for each ray: C-Ray: Incident rays perpendicular to the curved mirror will have a virtual ray passing through the C. P-Ray: Incident rays parallel to the principal axis reflect so that the virtual ray passes through the virtual focal point. F-Ray: Incident rays that point towards the virtual focal point before striking the mirror reflect from the mirror parallel to the principal axis.

Image Formation with a Convex Mirror A convex mirror has a virtual focus: f = -1/2xC http://class.phys.psu.edu/hopkins/Java/dmirr/index.html

Convex Mirror do ho di Focal length is negative Size: Smaller Attitude: Images will be upright Location: Behind mirror (- image distance) Type: Virtual hi ho di do

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