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1 Converging Lenses If we think of a double convex lens as consisting of prisms, we can see how light going through it converges at a focal point (assuming the lens is properly shaped).

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2 Diverging Lenses A double concave lens can also be modeled by prisms:

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3 Converging and Diverging Lenses

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Terminology of ConvexLenses Principal axis Optic axis Optical centre Principal Focus Secondary Focus Focal Length In reality, light bends twice at the air / glass boundaries On diagram, we show that light ray bends once: on the optic axis

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Concave Lens Terminology 5 Concave Lens is diverging. The Principal focus is virtual, in front of the lens.

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6 Principle Rays – Converging Lens Lens has two focal points because light can go both ways and still focuses on one spot

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Principle Rays – Converging Lens (Convex) 7 Incident RayReflected Ray Parallel to principal AxisThrough the focal point Parallel to principal Axis On the vertex of the lensGoes straight through and does NOT change direction

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8 Principle Rays – Diverging Lens Concave lens also has secondary focus, behind the lens. On diagrams, light rays also bend on the optic axis.

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Principle Rays – Diverging Lens (Concave) 9 Incident RayReflected Ray Parallel to principal AxisThrough the focal point Aiming the secondary focal pointParallel to principal Axis On the vertex of the lensGoes straight through and does NOT change direction

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10 Ray Diagram - Converging Lens Location of the image of an object located at 2F

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11 Ray diagrams– Converging Lens Location the image of an object located in front of F

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12 Ray Diagram - Diverging Lens Your turn: Locate the image of an object located between F and 2F for a diverging lens

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13 Image Types – Convering Lens The convex lens forms different image types depending on where the object is located with respect to the focal point Ssize can be enlarged or reduced Aattitude can be inverted or upright Limage can be infront or behind the lens Timage can be real or virtual

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14 Image Types – Diverging Lens The concave lens forms same type of image no matter where object is located: Sreduced Aupright Lin front of the lens Tvirtual

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Concave Lens (Diverging) Object Location SIZEATTITUD E LOCATIONTYPE ArbitrarySmallerUprightSame side of lens as object Virtual Convex Lens (Converging) Object Location SIZEATTITUD E LOCATIONTYPE In front of FLargerUprightSame side of lens as object Virtual Between F and 2F LargerInvertedOpposite side beyond 2F Real At 2FEqualInvertedOpposite side at 2F Real Beyond 2FSmallerInvertedOpposite side between F and 2F Real As object moves away from convex lens, real image moves closer to lens When object is located at F, no image is formed (verify with ray diagram) Summary: Image Characteristics formed by Concave and Convex Lenses

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16 The Thin-Lens Equation Sign Convention Distances: positive for real negative for virtual Heights : positive above axis negative below axis

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17 The Thin-Lens Equation d o = the distance from the mirror to the object d i = the distance from the mirror to the image f = the focal length

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18 Focal Length f Object Distance d o Image Distance d i + Converging Lens (Convex) Object is in front of mirror Image is REAL (opposite side of object) - Diverging Lens (Concave) N/A. d o is always positive Image is VIRTUAL (same side as object) Sign conventions: LENS Equation

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19 Magnification Equation for LENS M M If |M| > 1, image is larger than object (enlarged) If |M| < 1, image is smaller than object (reduced) M > 0 for up-right images M < 0 for inverted images -

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