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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

Reflection: Convex & Concave Mirrors


The law of reflection
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


Let s put the fun back in fundamentals
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.


Convex mirrors

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


Consider objects before a convex mirror we will trace three lines

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


Another example

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 !


Concave mirrors
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


An example of concave mirror
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


A different example of a concave mirror
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


A different example of a concave mirror1
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


A different example of a concave mirror2
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

?

?

?


A final example of a concave mirror
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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