Part 3: Optics (Lenses and Mirrors) LIGHT Part 3: Optics (Lenses and Mirrors)

Key Terms Convex: converging; has a surface that bulges outward Concave: diverging; has a surface that bulges inward Focal point: the point on the axis of a lens or mirror to which parallel rays of light converge Center of curvature: length equivalent to the radius of the mirror/lens Vertex: center of the curve of the mirror Principle Axis: line that passes through the center of the lens, perpendicular to the lens surface

Images can be…. Image: a picture or appearance of a real object formed by light that is reflected or refracted and can be categorized as either real or virtual Inverted: upside-down from the original object ( Up-Right: The same orientation as the original object Real image: image formed by diverging light rays; has a positive image distance (will be upside down) Virtual image: image formed by converging light rays; has a negative image distance (will be up-right) Larger or smaller than original object

1/do + 1/di = 1/f Lens and Mirror Equation do = object distance f = focal length (distance from the focal point to the center of the lens) positive for concave mirrors negative for convex mirrors do = object distance usually positive di = image distance can be + or –

Mirrors

Flat Mirror Images 1. virtual 2. upright 3. same size as object Images formed by flat mirrors are always: 1. virtual (virtual images are always behind mirrors) 2. upright (virtual images are always upright) 3. same size as object (if the image is larger or smaller, the mirror isn’t flat) 4. Left and right are reversed 5. located as far behind the mirror as the object is in front

To see your full body in a mirror, how tall MUST the mirror be?

Plane Mirror You only need a mirror ½ your height to see your whole body!! This is because of the law of reflection

LENSES

Note: Light always bends toward thickest part of lens transparent material that refracts light to form an image Focal Length Converging Lens Diverging Lens F F f Focal Point f (Convex) (Concave) Note: Light always bends toward thickest part of lens

Real Image formed by actual convergence of light rays Usually inverted Converging Lens F f (Convex)

Virtual Image formed by apparent convergence of light rays Usually right-side-up Diverging Lens F f (Concave)

Diverging Lens (Double Concave) Diverging Lens spread the light waves apart from each other Virtual focus Focus = - Can form only virtual, upright and smaller images

Enlarged virtual images Converging Lens (Double Convex) Converging Lens bring the light waves together to meet at a single point Principle focus Parallel rays Focus = + Can form real images (enlarged or reduced & inverted) or Enlarged virtual images

Rays Diagrams for Converging Lens (Double Convex) A ray thru the Center of the lenses Parallel ray Passes thru The focus focus (f) 2 f x Remains unbent Focal ray Refracts parallel To principal axis

Light passes through a lens Ray Tracing for Lenses Light passes through a lens There is a focal point on both sides of a lens Ray #1: Parallel to the axis Refracts through F Converging Lens: Ray #2: Through F Refracts parallel to axis Ray #3: Through Center of lens undeflected

Object Beyond 2f Converging Lens Image is: Real Inverted Reduced Appears between f and 2f Parallel ray focus (f) 2 f x Focal ray Object beyond 2f

Example: Camera

Object at 2f Converging Lens Image is: Real Inverted Same size Appears between f and 2f Parallel ray focus (f) 2 f x Focal ray Object at 2f

Object Between 2f & f Converging Lens Image is: Real Inverted Enlarged Appears beyond 2f Parallel ray focus (f) 2 f x Focal ray Object between f and 2f

Example: Slide Projector

Object Between f &Converging Lens Image is: Virtual Erect Enlarged Appears on same Side as Object Apparent Convergence Of rays focus (f) 2 f x Object Inside focus

* Convergent lenses can produce real or virtual images Example: Magnifying Glass Web Link: Ray tracing

Object at f Image is: Not formed focus (f) 2 f x Object at the focus

In summary: If an object is at the focal point, there is not image formed. If an object is between the focal point and the lens, the image is virtual. If an object is beyond that focal point, the image is real.

1/do + 1/di = 1/f Reminder: Lens and Mirror Equation f = focal length (distance from the focal point to the center of the lens) positive for convex lenses negative for concave lenses do = object distance usually positive di = image distance can be + or –

Sign conventions for Lenses Focal length (f) + converging - diverging Object distance (do) + object on the left Image distance (di) + image on the right (real) - image on the left (virtual)

An object is placed 3 m from a convex lens with a focal length of 10 cm. How far from the lens does the image appear? 10 cm 3 m (not to scale)

= 0.103 m di Find LCD 1 = + f do di = 29 3 di 1 1 = + 0.1 3 di = 3 29 An object is placed 3 m from a convex lens with a focal length of 10 cm. How far from the lens does the image appear? 10 cm 3 m 1 = + f do di = 29 3 di 1 1 = + 0.1 3 di = 3 29 di 1 di = ? = - 1 0.1 3 di Find LCD do = 3 m f = 10 cm = 0.1 m = - 30 3 1 di = 0.103 m di

An object is placed 4 cm from a convex lens with a focal length of 10 cm. How far from the lens does the image appear? 4 cm 10 cm

= -6.67 cm di on same side as object! Find LCD 1 = + f do di = -3 20 An object is placed 4 cm from a convex lens with a focal length of 10 cm. How far from the lens does the image appear? 10 cm 4 cm 1 = + f do di = -3 20 di 1 1 = + 10 4 di di = ? = 20 -3 di 1 do = 4 cm = - 1 10 4 di on same side as object! Find LCD f = 10 cm = -6.67 cm di = - 2 20 5 di 1