Light as a ray Reflection

No light, no sight In darkened room, eyes to observe, brain to decipher, objects appear black Light reflects off of objects and travels in straight lines to our eyes. Demo: laser + mister

Line of sight Luminous objects radiate light in all directions. Illuminated objects reflects in mostly all directions. The both cases, the only portion you see is the tiny cone of light traveling in a straight line from the object to your eyeball. Radiare: L: radius, ray or spoke

Image location in plane mirror 5.Move your eye to a new location and repeat steps 2 and 3 two or more times. 6.Remove the mirror. Extend the lines using dashes until they intersect behind the plane of the mirror. 7.Use a straight edge to draw a line between the object and the point where each line crosses the mirror. 1.Place a narrow object (e.g., a pin) on a piece of paper in front of upright plane mirror. 2.Draw a line where the base of the mirror touches the paper. 3.With your eye at mirror level, place three pins so they line up with your view of the image. 4.Remove the pins. Connect the dots using a straight edge.

Law of reflection Objects reflect light in every direction. The reason we see objects is because some of the light reaches our eyes. Incident ray Reflected ray

Note: The triangle formed by object, point of reflection, and the distance from mirror is similar to triangle formed by the image, point of reflection and the distance from the mirror. object image

Implications object image

Law of reflection

Image formation

What’s wrong with these models?

Think about it… A ray of light is incident towards a plane mirror at an angle of 30-degrees with the mirror surface. What will the angle of reflection be?

Think about it… Perhaps you have observed the image of the sun in the windows of distant buildings near the time that the sun is rising or setting. However, the image of the sun is not seen in the windows of distant building during midday. Use the diagram below to explain, drawing appropriate light rays on the diagram.

Specular reflection Once the normal to a surface is drawn and the angle of incidence is known, you can predict the angle of reflection: Horizontal surfaces Vertical surfaces Curved surfaces

Diffuse reflection Reflection off rough surfaces follows the law of reflection too… but does not produce a coherent image.

Application Oncoming traffic on wet roads at night

Application Pretty pictures of things reflected in lakes

Image formation in plane mirrors 1.Images are virtual i.e., light appears to come from behind the mirror (but does not) 2.Images are upright 3.Images are left-right reversed 4.Images have a magnification of 1 Object distance = image distance Object size = image size

Ray diagram: 1 of 3

Ray diagram: 2 of 3

Ray diagram: 3 of 3 5.Repeat steps 3 & 4 for other extremities

How tall does a mirror need to be?

Spherical mirrors It is frequently useful to reflect light and increase the image size or increase the intensity of light reflected from a mirror. For those applications, we use spherical mirrors.

Anatomy of spherical mirrors If we imagine the mirror as a slice of a sphere, then… Principal axis: imaginary line from center of sphere Center of curvature: center of sphere Focal point: midway between center of curvature and point where principal axis intersects mirror Focal length: distance from mirror to focal point.

Spherical mirrors All light reflected off a spherical concave mirror passes through the focal point. Light can be intense at focal point!

Concave mirrors Depending on the object location, the image may be Enlarged or reduced Upright or inverted Real or virtual

Concave mirrors For a concave mirror, the normal at the point of incidence on the mirror surface is a line that extends through the center of curvature. The angle of incidence can be measured and the reflected ray can be drawn with the same angle. In real life

Ray diagram: 1 of 4 1.Draw the object the appropriate height and distance from the mirror. 2.Draw the mirror 3.Draw the principal axis 4.Label the center of curvature, C 5.Label the focal point, f Cf

Ray diagram: 2 of 4 6.Draw incident ray 1 from extremity of object parallel to principal axis 7.Draw reflected ray 1 from mirror through focal point Cf

Ray diagram: 3 of 4 8.Draw incident ray 2 from extremity of object through the focal point 9.Draw reflected ray 2 from mirror through focal point Cf

Ray diagram: 4 of 4 10.Draw incident ray 3 from extremity of object through the center of curvature 11.Draw reflected ray 3 from mirror through the center of curvature 12.The image will form where the reflected rays converge (or appear to converge) Cf

When d object > C When the object is outside the radius of curvature, notice that the image is smaller and inverted. Notice too that light rays actually converge. The image can be projected and is considered “real”

When d object f When you bring an object between the center of curvature and the focal point, notice the image is larger, inverted, and real.

When d object < f Cf When you bring an object closer than the focal point, the image is larger, upright, and virtual.

When d object = f Cf When you place an object at the focal point, the image never forms.

Summary

Convex mirrors Images formed by convex mirrors are always smaller, upright, and virtual. In real life

Mathematical models Ray diagrams are useful for providing information about relative location and size, orientation, and type of image. They are less useful for quantifying that information. We use the Mirror Equation.

Mirror equation – part 1 h0h0 hihi object image

Mirror equation – in process h0h0 hihi object other

Mirror equation – part 2 h0h0 hihi object other

Example A 1.5-cm high object is placed 20 cm in front of a concave mirror with a focal length of 15 cm. Position of image? Try it first.

Example Suppose you place an object 10 cm in front of a mirror with a focal length of 0.1 m. At what distance will the image appear? Try it first.

Magnification

Example A 1.5-cm high object is placed 20 cm in front of a concave mirror with a focal length of 15 cm. The image forms 60 cm away. Size of image? Try it first.

Example A side view car mirror is convex with a radius of 16.0 m. Determine the location of the image for an object 10.0 m from the mirror. Try it first.

Summary of mathematical relationships Relationship between height and distance Relationship between focal length and distance Relationship between magnification, height, and distance