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Curved Mirrors Chapter 13 Section 3

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Mirror Terminology Ccenter of curvature Rradius of curvature

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Mirror Terminology Virtual image – produced at a point where light rays appear to come from Real image – produced when rays of light intersect (can be displayed on a surface)

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Mirror Terminology pobject distance qimage distance

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Mirror Terminology hobject height h’image height

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Mirror Terminology Inverted Upright

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Mirror Terminology Ffocal point ffocal length (also equal to ½ R)

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Concave Mirrors Curved inward Converges light rays Used to produce magnified virtual images Can also produce real images Example use = make-up mirror

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Convex Mirrors Outwardly curved Diverges light rays Image is always virtual Image distance is always negative Focal length is always negative

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Uses of Convex Mirrors Can provide a view of a large area (like in a convenience store) Used on passenger side-view mirrors with the warning “objects are closer than they appear”

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Ray diagrams for curved mirrors 1. Tip of object to mirror parallel to principal axis (reflects through focal point) 2. Tip of object on a line that contains the focal point (reflects parallel to principal axis) 3. Tip of object through center of curvature (reflects back along itself)

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Mirror Conventions In front (of a mirror) = left Displacements to the left of a mirror are + Displacements to the right of the mirror are – Example: q is +when the image is real but - when the image is virtual Displacements above the principal axis are + Displacements below the principal axis are – Example: h’ is + when the image is upright and – when the image is inverted

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Mirror Equation Can be used to predict image location 1/p + 1/q = 1/f

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Magnification Equation Relates image size to object size M<1 = image smaller than object M>1 = image larger than object M is - when image is inverted M is + when image is upright M = h’ = - q h p h p

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#1 The surface of a concave mirror is pointed towards the sun. Light from the sun hits the mirror and converges to a point. How far is this converging point from the mirror's surface if the radius of curvature (R) of the mirror is 150 cm?

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#1 Answer Hint: What is the relationship between the center of curvature and the focal point of a mirror? R = 2f Because R = 150, f = 75 cm

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#2 If p=7cm and q=3cm, find f.

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#2 Answer f = 2.1 cm The positive value for f tells us that this is a concave mirror.

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#3 If the object is 5cm from a mirror whose focal point is 10 cm, what will the image distance be?

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#3 Answer q = -10 cm The negative sign tells us that the image is… virtual

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#4 Calculate the image height of an 8 cm object when p = 12 cm and q = 3 cm.

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#4 Answer h‘ = - 2 cm Because h’ is less than h, the image is… reduced Because the h’ value is negative, the image is… inverted

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#5 The image formed by a concave mirror is upright and virtual. What would be the signs for R, f, q, and h’?

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#5 Answer What would be the signs for R, f, q, and h’? R is + because this is a concave mirror f is + because this is a concave mirror q is – because the image is virtual h‘ is + because the image is upright

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