General Physics II Mirrors & Lenses
Nothing New! For the next several lectures we will be studying geometrical optics. You already know the fundamentals of what is going on!!! Reflection: θ 1 = θ r incident ray reflected ray θ 1 θ r n 1 Refraction: n = n 1 sinθ1 2 sin θ 2 θ 2 n 2 refracted ray We will use these laws to understand the properties of mirrors (perfect reflection) and lenses (perfect refraction). We will also discover properties of combinations of lenses which will allow us to understand such applications as microscopes, telescopes, and eyeglasses.
Images formed by mirrors and lenses may be classified as real or virtual. Real Image formed by actual rays of converging light Virtual Image not formed by actual rays of converging light, but from where the rays of light appear to come (diverging light rays)
Reflection at a plane surface d o h o h i d i image is upright image is virtual No Magnification (h o = h i ) d i = d o
Reflection at a plane surface more Light rays radiate from a point object at P in all directions and obey the Law of Reflection upon interaction with the mirror. P The reflected rays entering the eye look as though they had come from the image.
Spherical mirrors There are two types of spherical mirrors + - + - (where reflected rays go) (dark side) (where reflected rays go) (dark side) concave convex shiny Focal length, f, is positive shiny Focal length, f, is negative
Parts of a Spherical Concave Mirror The focal length is half of the radius of curvature. + - The focal length is positive for this type of mirror. Center Focus R f Principle axis R = 2f
Parts of a Spherical Convex Mirror The focal length is half of the radius of curvature, and both are on the dark side of the mirror. The focal length is negative for this type of mirror. + - R f Focus Center Principle axis
Images for Concave Spherical Mirrors Parallel Ray: Draw a ray from the tip of the arrow parallel to the principle axis. Upon striking the mirror, it reflects back and passes through the focal point (F) of the mirror. C F Focal Ray: Draw a ray from the tip of the arrow through the focal point. Upon striking the mirror, this ray is reflected back parallel to the principle axis. It is where the REFLECTED rays intersect that the image is formed!!
Images for a Convex Spherical Mirror Parallel Ray: Draw a ray from the tip of the arrow parallel to the axis. Upon striking the mirror, this ray reflects back along a line that appears to pass through the focal point. Focal Ray: Draw a ray from the tip of the arrow toward the focal point. Upon striking the mirror, this ray is reflected back parallel to the axis. It is where the REFLECTED rays intersect that the image is formed!!
The Mirror Equation 1 d o + 1 di = 1 f O F f I d o d i O d o d i f I F Now, we can introduce a sign convention. We can indicate that this image is inverted if we define its magnification M as the negative number given by: M = d d i o
Lenses A lens is a piece of transparent material shaped such that parallel light rays are refracted towards a point, a focus: Convergent Lens (Convex) light moving from air into glass will move toward the normal light moving from glass back into air will move away from the normal real focus Divergent Lens (Concave) light moving from air into glass will move toward the normal light moving from glass back into air will move away from the normal virtual focus Negative f Positive f
Images for a Convex Converging Lens Parallel Ray: Draw a ray from the tip of the arrow parallel to the principle axis. Upon REFRACTION, it passes through the focal point on the opposite side of the lens. Focal Ray: Draw a ray from the tip of the arrow through the focal point on the same side of the lens. Upon REFRACTION, this ray moves parallel to the principle axis. It is where the REFRACTED rays intersect that the image is formed!!
Images for a Concave Diverging Lens Parallel Ray: Draw a ray from the tip of the object parallel to the principle axis. Upon REFRACTION, it moves along a line that appears to have come from the focal point on the object s side of the lens. Focal Ray: Draw a ray from the tip of the object directed toward the focal point on the opposite side of the lens. Upon REFRACTION, this ray moves parallel to the principle axis. It is where the REFRACTED rays intersect that the image is formed!!
The Lens Equation.same as the Mirror O F F d i d o f I 1 d o + 1 di = 1 f M = d d i o O F I F d i f d o
End of Mirrors & Lenses Lecture