5 ConcaveMirrors.notebook January 28, 2021

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Images in Concave

Mirrors

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• Curved mirrors are created when you make part of the surface of a sphere reflective.

Concave Mirrors – reflection from inner surface of sphere

Convex Mirror – reflection is from the outer surface of the mirror.

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Concave mirror

•A mirror whose reflecting surface curve

inward

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Principal axis

•The line that passes through the centre of

curvature, C

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Centre of Curvature

•The point at which all of the normals meet

•If an incident ray passes through this point its

reflected ray bounces directly back along the same

path

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Focal Point

•On the principal axis

•When the incident ray is near and parallel to the

principal axis, the reflected ray passes through this

point

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Focal Length

•The distance, along the principal axis, from the

focal point to the mirror

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Drawing Ray Diagrams

•The image formed by a concave mirror is dependent

upon the location of the object

•The steps for drawing the image are always the same

There are FIVE possible outcomes for concave

mirrors, but only three produce visible images

•The object can be:

– between the focal point and the mirror – between the centre of curvature and the focal point – beyond the centre of curvature The objects we will look at always have one end on the principal axis

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Case 1 Objects between the

focal point and the mirror

•Step 1

–label the focus (f) and center of curvature (c) –Draw the object so that one end is on the principal axis *this may already be done for you *it will be beneficial to use arrows when drawing rays

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•Step 2

–Draw an incident ray from the top of the object to the mirror –Make sure it’s parallel to the principal axis –Draw the reflected ray remember that it goes through the focal point

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•Step 3

–Draw an incident ray through the focal point and the top of the object to the mirror –Draw the reflected ray –Remember that it will be parallel to the principal axis

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•Step 4

•Draw an incident ray through the centre of

curvature and the top of the object to the mirror

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•An image only forms where the reflected

rays intersect.

•If the rays do not intersect in front of the

mirror, the reflected rays may need to be

extended behind the mirror.

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•Step 5

•Draw the image

•The top of the image is at the intersection of

the reflected rays

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Remember to state the

characteristics of the image

•Location (in front or behind the mirror)

•Orientation (upside down or right side up)

•Size (larger, smaller or the same as original)

•Type (virtual or real)

•L O S T

(magnification)

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Case 2 Objects between the Focus and

the Center of Curvature

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Case 3 Objects between beyond the

Center of Curvature

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MIRROR and MAGNIFICATION

EQUATIONS

}

So far, we have been determining the

characteristics of images by drawing ray

diagrams for concave and convex mirrors.

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The mirror and magnification equations allows

you to calculate these characteristics.

Math Review

fractions

solving equations

put the two together

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Allows you to calculate the location of the

image, without having to draw a diagram.

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The image distance, d

_i

, is negative if the

image is behind the mirror (a virtual image)

Mirror Equation

1 = 1 + 1

f d

_i

d

_o

Where:

f - focal length (from focus to mirror) di – image distance (from image to mirror)

do – object distance (from object to mirror)

"f"

"d

_i

"

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}A concave mirror has a focal length of 12 cm. An

object with a height of 2.5 cm is placed 40.0 cm in front of the mirror. Calculate the image height.

Example

1 = 1 + 1 f d_i d_o 1 = 1 - 1 d_i f d_o 1 = 1 - 1 d_i 12 cm 40 cm = 10 - 3 120 cm 120 cm Lowest common denominator 1 = 7 d_i 120 cm d_i = 120 cm 7 d_i= 17.14 cm

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}

The magnification equation allows you to find

the magnification from the object and image

distances.

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The image height, h

i

, is negative if the image

is inverted relative to the object.

Magnification Equation

magnification = the ratio of the heights or the distances

A magnification of 2 would mean the image is twice as large as the object.

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}A concave mirror has a focal length of 12 cm. An object with a height of 2.5 cm is placed 40.0 cm in front of the mirror. Calculate the image height.

The height of the image is 1.07 cm. The image height is negative, so the image is inverted.

Example con't

h

_i

= -d

_i

h

_o

d

_o

h

_i

=

-17.14 2.5 cm

40.0 h_i = 2.5 cm (-17.14) 40.0 h_i = -1.07 cm

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1.

A concave mirror has a focal length of 6.0 cm.

An object with a height of 0.60 cm is placed 10.0

cm in front of the mirror.

a.Calculate the image distance.

b.Calculate the image height.

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26 F 2 cm C 4 cm 1 cm 1 cm

1.

In the diagram below, the object is between the

mirror and F. Use the data in the diagram to answer

the questions below. (Diagram is not to scale.)

a.Calculate the image distance

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Mirrors and Magnification Equations

Magnification

– the change in size of an optically produced image

Mirror Equation

•f = •di = •do = the focal length the distance of the image from the mirror the distance of the object from the mirror

"f"

"d

_i

"

"d

o

"

Negative value for this case.