Reflection

When a wave changes media, some of it is reflected back. The amount of reflection depends on how different the media are.

Angle of Incidence = Angle of Reflection Light reflected from a plane (flat) mirror follows the Law of Reflection: These angles are measured from the normal, a line perpendicular to the mirror. Angle of Incidence = Angle of Reflection Ɵi = Ɵr

Questions: Why can you not see yourself in all flat surfaces Questions: Why can you not see yourself in all flat surfaces? The paper is rough and gives irregular reflections.

Ray Diagrams When you look at an image in a plane mirror it is: The same size. hi = ho The same distance behind the mirror (virtual image) as you are in front of it. di = -do Right side up and laterally inverted. Also, the reflected light has the same speed, wavelength and frequency as the incident light.

When drawing ray diagrams we draw two rays of light coming from the object, reflecting and then heading to the observer.

Questions: What minimum length of mirror do you need to obtain a full length view of yourself? You need a mirror half your height.

Curved Mirrors Concave mirrors are curved (“caved”) inwards Convex mirrors are curved outwards

Since the surfaces are curved, the normal is different at different points.

Concave Mirrors Principle axis: straight line perpendicular to the mirror Centre of curvature (C): the point that represents the center of the sphere Focal point (F): point where all of the reflected rays meet Focal length (f): distance from the focal point to the mirror

Consider the situation where an object is beyond the center of curvature: Remember: any ray of light traveling parallel to the principal axis will reflect through the focal point. The image is real, smaller and inverted.

Now consider if the object is at C Now consider if the object is at C. The image is real, equal and inverted.

Now consider if the object were between C and F: The image is real, inverted and larger.

Now consider if the object is at F: The image is “at infinity”, i. e Now consider if the object is at F: The image is “at infinity”, i.e. it can never be seen.

Finally consider the case where the image is within the focal point, F: The image is virtual, larger and upright.

Convex Mirrors Convex mirrors reflect light from their outside surface. Because of this the reflected rays always diverge. Since there is no true focal point it is placed behind the mirror

Consider an object at any point in front of a convex mirror Consider an object at any point in front of a convex mirror. The image is always virtual, smaller and upright!

The (Spherical) Mirror Equation 1 𝑓 = 1 𝑑 𝑖 + 1 𝑑 𝑜 Where f is the focal length, di is the distance of the image to the mirror and do is the distance of the object to the mirror. Note that for a spherical mirror the focal length is half of the mirror’s radius of curvature. 𝑓= 𝑟 2

Magnification by a Spherical Mirror 𝑚≔ ℎ 𝑖 ℎ 𝑜 =− 𝑑 𝑖 𝑑 𝑜 Where m is the magnification, hi is the height of the image and ho is the height of the object. The variables di and do are as before. Found from similar triangles.

Example 1 A 2 cm tall object is 12 cm away from a concave mirror with a focal length of 8 cm. Determine the height and position of the image. Verify with a ray diagram.

Example 2 A convex security mirror has a -0.40 m focal length. A 1.8 m high person stands 6 m from the mirror. What are the image’s position and height? Verify with a ray diagram.