Formation of Images by Spherical Mirrors

For an object infinitely far away (the sun or starts), the rays would be precisely parallel.

If a mirror is small compared to its radius of curvature, so that the reflected rays make only a small angle upon reflection, then the rays will cross each other at a single point, or focus.

The principal axis of a mirror is defined as the straight line perpendicular to the curved surface at its center.

The point F, where the rays parallel to the principal axis, come to a focus, is called the focal point of the mirror.

The distance between focal point and the center of the mirror is called the focal length, f, of the mirror.

Another way of defining the focal point is to say that it is the image point for an object infinitely far away along the principal axis.

Finding the Image Position for a Curved Mirror

-ray 1 is drawn parallel to the axis; therefore it must pass along a line through F; -ray 2 is drawn through F, as result is must reflect into parallel to the principal axis ray; -ray 3 is chosen to be perpendicular to the mirror, and so is drawn so that it passes through C, the center of curvature; it will be reflected back on itself.

Mirror Equation

The lateral magnification, m, of a mirror is defined as the height of the image divided by the height of the object:

The Sign Convention -the image height h i is positive if the image is upright, and negative if inverted, relative to the object; -d i and d o are both positive if image and object are on the reflecting side of mirror, but if either image or object are behind the mirror, the corresponding distance is negative.

1.You hold a small light bulb directly in front of a concave mirror beyond the mirror focal point. Is it possible for two rays leaving the light bulb to intersect after reflecting from the mirror? Is the bulb image real or virtual? Explain. 2.Can the image produced by a convex mirror ever be larger than the object? Why? 3.Most of us find that we really have to strain our eyes to focus on objects located close to our noses. You hold two mirrors 1 foot in front of your face. One is a plane mirror, and the other is a concave mirror with a 3-inch focal length. In which case are you more likely to have tp strain your eyes to see the image of your nose?

1.What type of mirror would you use to produce a magnified image of your face/ 2.The image produced by a convex mirror is always closer to the mirror than the object. Then why is it that the convex mirrors used on cars and trucks often have the warning: “Caution: Objects Are Closer Than They Appear” printed on them? 3.What are the size and location of the image of your face when you hold your face very close to a concave mirror? How do the size and location change as you move away from the mirror?

Index of Refraction

The ratio of the speed of light in vacuum to the speed of light v in a given material is called the index of refraction, n of the material: n=c/v

If the light enters the medium where the speed of light is less, it bends toward the normal. If light travels from one medium into a second where its speed is greater, the ray bends away from the normal.

Snell’s Law

Total Internal Reflection

Important: total internal reflection can occur only when light strikes a boundary where the medium beyond has a lower index of refraction.

Total Internal Reflection: Applications