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Chapter 36

Chapter 36. Image Formation 1: Flat mirror Spherical mirrors. Notation for Mirrors and Lenses. Object : that emits light. Image : that forms in our brain. Magnification : The ratio of the size of the image to the size of the object. . Notation for Mirrors and Lenses.

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Chapter 36

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  1. Chapter 36 Image Formation 1: Flat mirror Spherical mirrors

  2. Notation for Mirrors and Lenses • Object : that emits light. • Image : that forms in our brain. • Magnification : The ratio of the size of the image to the size of the object.

  3. Notation for Mirrors and Lenses • The object distance is the distance from the object to the mirror or lens • Denoted by p • The image distance is the distance from the image to the mirror or lens • Denoted by q • The (lateral) magnification of the mirror or lens is the ratio of the image height to the object height • Denoted by M,

  4. Types of Images • A real image is formed when light rays pass through and diverge from the image point • Real images can be displayed on screens • A virtual image is formed when light rays do not pass through the image point but only appear to diverge from that point • Virtual images cannot be displayed on screens

  5. Images Formed by Flat Mirrors • Simplest possible mirror • Light rays leave the source and are reflected from the mirror • Point I is called the image of the object at point O • The image is virtual

  6. Find Images Formed by Flat Mirrors • One ray starts at point P, travels to Q and reflects back on itself • Another ray follows the path PR and reflects according to the law of reflection • One can prove that and

  7. Reversals in a Flat Mirror • A flat mirror produces an image that has an apparent left-right reversal • For example, if you raise your right hand the image you see raises its left hand • The reversal is not actually a left-right reversal • The reversal is actually a front-back reversal • It is caused by the light rays going forward toward the mirror and then reflecting back from it

  8. Properties of the Image Formed by a Flat Mirror – Summary • The image is as far behind the mirror as the object is in front • |p| = |q| • The image is unmagnified • The image height is the same as the object height • h’ = h and M = +1 • The image is virtual • The image is upright • It has the same orientation as the object • There is a front-back reversal in the image

  9. Example • What is the minimum length of a flat mirror so that you can see yourself full height in the mirror? • What is the minimum length of a flat mirror so that you can see another person’s full height in the mirror?

  10. Another example • Determine the image distances of the first and second order images with respect to their own mirror. 1 m 3 m A B

  11. Spherical Mirrors • A spherical mirror has the shape of a section of a sphere • A concave spherical mirror has the silvered surface of the mirror on the inner, or concave, side of the curve • A convex spherical mirror has the silvered surface of the mirror on the outer, or convex, side of the curve

  12. Concave Mirror, Notation • The mirror has a radius of curvature of R • Its center of curvature is the point C • Point V is the center of the spherical segment • A line drawn from C to V is called the principal axis of the mirror

  13. Paraxial Rays • We use only rays that are close to the principal axis • Such rays are called paraxial rays • This is the case when the mirror radius is very large compared to the size of the mirror

  14. Focal Length • When paraxial rays are parallel with the principal axis, they reflect on the mirror and meet at one point on the principal axis. • This point (the image of these parallel rays) is called the focal point • The distance from the mirror to the focal point is called the focal length • It can be proved that the focal length is ½ the radius of curvature

  15. Focal Length

  16. Focal Point • The colored beams are traveling parallel to the principal axis • The mirror reflects all three beams to the focal point • The focal point is where all the beams intersect • It is the white point

  17. Find the image • Method 1: the ray diagram Ray 3 begins as an incident ray that passes through the center of curvature, strikes the mirror perpendicularly, and reflects back, moving along the same line as the incident ray. Ray 1 starts as an incident ray that is parallel to the principal axis. It reflects off the mirror and passes through the focal point after it reflects. Ray 2 starts as an incident ray that passes through the focal point and then reflects parallel to the principal axis.

  18. The ray diagram Ray 3 begins as an incident ray that passes through the center of curvature, strikes the mirror perpendicularly, and reflects back, moving along the same line as the incident ray. Ray 2 starts as an incident ray that passes through the focal point and then reflects parallel to the principal axis. Ray 1 starts as an incident ray that is parallel to the principal axis. It reflects off the mirror and passes through the focal point after it reflects. Image up-side-down, smaller, real

  19. Object locations and their images

  20. Convex Mirrors • A convex mirror is sometimes called a diverging mirror • The light reflects from the outer, convex side • The rays from any point on the object diverge after reflection as though they were coming from some point behind the mirror • The image is virtual because the reflected rays only appear to originate at the image point

  21. Find the image • Method 1: the ray diagram Ray 1. Ray 1 is incident parallel to the principal axis. If we extend the reflected component of this ray backward through the mirror, the virtual ray will pass through the focal point. Ray 2. Instead of passing through the focal point, the incident part of ray 2 is directed toward it. Before it can reach the focal point behind the mirror, it reflects parallel to the principal axis. Its virtual extension behind the mirror is also parallel to the axis. Ray 3. The incident component of Ray 3 is directed toward the center of curvature on the far side of the mirror and reflects back along the same line. The virtual extension of the reflected ray passes through the center of curvature.

  22. Only one case for a diverging mirror Image always upright, smaller, virtual

  23. Notes on Images • With a concave mirror, the image may be either real or virtual • When the object is outside the focal point, the image is real • When the object is at the focal point, the image is infinitely far away • When the object is between the mirror and the focal point, the image is virtual • With a convex mirror, the image is always virtual and upright • As the object distance decreases, the virtual image increases in size

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