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Reflection: Convex & Concave Mirrors

Reflection: Convex & Concave Mirrors. The Law of Reflection. Regardless of whether we are dealing with a plane mirror (flat) or a concave (bent in) mirror, or convex (belly out) mirror, the law of reflection still holds…

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Reflection: Convex & Concave Mirrors

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  1. Reflection: Convex & Concave Mirrors

  2. The Law of Reflection • Regardless of whether we are dealing with a plane mirror (flat) or a concave (bent in) mirror, or convex (belly out) mirror, the law of reflection still holds… • θ’ = θi where θ’ is the angle or reflection equal to θi the angle of incidence

  3. Let’s put the “fun” back in fundamentals! • Let us first remember that all mirrors have a focal point (F). • Positive F for concave, negative F for convex mirrors. (Just the OPPOSITE of lenses.) • The focal length (f) is equal to ½ the radius of curvature (R). • “R” measures from the center (C) of a circle to it’s surface.

  4. F C Convex Mirrors • Curve away from you with a “belly out” look. • The silvered side is considered negative. • Convex mirrors have a negative focus. Back is negative Front is positive

  5. F C Consider objects before a convex mirror…we will trace three lines. 1st: POA Principle Optic Axis(through F and C, then back on itself) 2nd: Head to Center(any line to the center will come back on itself) 3rd: Head to POA (such that angle of reflection is equal to angle of incidence) Notice that lines 2 and 3 do not actually intersect… but draw line 3 back from where it appears to originate, and lines 2 and 3 intersect behind the mirror to form an imaginary image (shown in green). 2 1 θi θ’ = θi 3 larger erect The image is thus… imaginary (-) equal real (+) inverted smaller s c i

  6. F C Another example… • 1st: POA Principal Optic Axis (through negative F, to C and back) • 2nd: From Head (to C and back) • 3rd: From Head to POA (where θ’ = θiRemember! Line 3 is drawn back if there is no actual intersection in front of mirror) 3 1 θ’ = θi θi erect because BOTH point the same way…down 2 larger equal real (front) imaginary (back) The image is thus… erect inverted smaller s c i Images for convex mirrors are ALWAYS s c i !

  7. Concave Mirrors • Curve toward you with a “cave in” look. • The silvered side is considered negative. • Concave mirrors therefore have a positive focus. Back is negative F C Front is positive

  8. An example of concave mirror… • 1st: POA Principal Optic Axis (through positive F, to C and back) • 2nd: From Head (to C and back) • 3rd: From Head to POA (where θ’ = θi) 3 θ’ = θi F C 1 θi 2 inverted since the image points in the opposite direction of object larger equal real (front) imaginary (back) The image is thus… erect inverted smaller s v r

  9. A different example of a concave mirror… 3 • 1st: POA Principal Optic Axis (through positive F, to C and back) • 2nd: From Head (to C and back) • 3rd: From Head to POA (where θ’ = θi) inverted since the image points in the opposite direction of object C θ’ = θi 1 θi F 2 imaginary (back) real (front) larger erect The image is thus… equal inverted smaller e v r

  10. A different example of a concave mirror… • 1st: POA Principal Optic Axis (through positive F, to C and back) • 2nd: From Head (to C and back) • 3rd: From Head to POA (where θ’ = θi) θi F C 1 θ’ = θi inverted since the image points in the opposite direction of the object 2 imaginary (back) real (front) 3 larger erect The image is thus… equal inverted smaller l v r

  11. A different example of a concave mirror… • 1st: POA Principal Optic Axis (through positive F, to C and back) • 2nd: From Head (to C and back) • 3rd: From Head to POA (where θ’ = θi) NO image forms since the reflected rays NEVER meet because they are parallel 1 C θi θ’ = θi F 2 imaginary (back) real (front) 3 larger erect The image is thus… equal inverted smaller ? ? ?

  12. A final example of a concave mirror… • 1st: POA Principal Optic Axis (through positive F, to C and back) • 2nd: From Head (to C and back) • 3rd: From Head to POA (where θ’ = θi) Notice that lines 2 and 3 do not meet… But they are NOT parallel… So draw them from where they appear to come from. θi F C 1 2 θ’ = θi 3 real (front) imaginary (back) larger erect The image is thus… equal inverted smaller l c i

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