 # Curved Mirrors. Two types of curved mirrors 1. Concave mirrors – inwardly curved inner surface that converges incoming light rays. 2. Convex Mirrors –

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Curved Mirrors

Two types of curved mirrors 1. Concave mirrors – inwardly curved inner surface that converges incoming light rays. 2. Convex Mirrors – outwardly curved, mirrored surface that diverges incoming light rays.

Concave mirrors… can form BOTH virtual and real images of an object depending on how far the object is placed away from the mirror. can form BOTH virtual and real images of an object depending on how far the object is placed away from the mirror. Real image: an image formed when light rays intersect at a single point. Real image: an image formed when light rays intersect at a single point.

Image location can be predicted with mirror equations. Image location can be predicted with mirror equations. Concave mirrors Principal axisCenter of Curvature ( C ) Focal Length ( f ) Object distance ( p ) h 1/object distance + 1/image distance = 1/focal length 1/p + 1/q = 1/f

Images produced by concave mirrors (virtual or real) will NOT be the same size of our object. Images produced by concave mirrors (virtual or real) will NOT be the same size of our object. They will be magnified (M) They will be magnified (M) magnification = image height = - image distance magnification = image height = - image distance object height object distance object height object distance M = h'/h = - q/p + M = upright and virtual image - M = inverted and real image Concave mirrors

Rules for drawing reference lines Ray Line from object Line from mirror to to mirror reflected image to mirror reflected image 1. Parallel to principal Through focal point axis F axis F 2. Through focal point parallel to principal F axis F axis 3. Through the center back along itself through of curvature C C of curvature C C

Object distance is greater than the focal length Principal axis Reflecting Surface Ray Diagram fC

Object distance is less than the focal length Principal axis Reflecting Surface Ray Diagram fC

Convex Mirrors Focal point and center of curvature are located behind the mirror’s surface. Focal point and center of curvature are located behind the mirror’s surface. Magnification (M) is always +, but it is less than 1 Magnification (M) is always +, but it is less than 1 Image is always virtual Provide a large field of view Provide a large field of view

Convex Mirrors Principal axis fC Reflecting Surface

Lens Characteristics  Lenses are objects that refract light rays. Converging LensDiverging Lens  Two refracting surfaces  Rays will either converge or diverge to create an image.  Two Types:

Lens Characteristics f fff

Converging Lenses   Produce either real or virtual images   Object distance > f = real image, opposite side   Object placed closer than f = virtual image, same side   Object placed at infinity = point image on opposite f (ex. Sun & magnifying glass) pg. 571 Fig. 15.3   Object at f = image at infinity (ex. Lighthouses) Fig. 15.3

Ray Diagram (Converging Lens) f f P-Axis 1 1. In parallel to P-axis, out to f point 2. To center of lens, out center of lens 3. Passes through f, out parallel to P-axis 2 3 Image THE HUMAN EYE

P-Axis f f 1 2 3 Image Ray Diagram (Converging Lens) Binoculars, microscopes, & telescopes

Diverging Lenses   Only produces virtual images on the same side as the object.   Object distance > f = image is larger   Object distance < f = image is smaller   Used to correct nearsightedness

Ray Diagram (Diverging Lens) f f 1. In parallel to P-axis, out away from f point 2. To center of lens, out center of lens 3. Travels towards opposite f, out parallel to P-axis Image 1 2 3

Thin Lens Equation   Is identical to the mirror equation and can be used for both convergent and divergent lenses. 1 + 1 = 1 do di f + do = object in front of lens - do = object behind lens + di = image behind lens - di = image in front of lens + f = converging lens - f = diverging lens

Magnification of a Lens   Formula is also identical to mirror magnification formula: M = hi = - di ho do + M = virtual, upright image - M = real, inverted image

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