 # Optics. Spherical Mirrors Spherical mirror – a section of a sphere of radius R and with a center of curvature C R C Mirror.

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Optics

Spherical Mirrors Spherical mirror – a section of a sphere of radius R and with a center of curvature C R C Mirror

Spherical Mirrors The radius (R) and center of curvature (C) of the sphere Principal axis – a line drawn through C to the mirror Vertex (V) – where the principal axis intersects the mirror The focal point (F) and focal length (f) R C Principal axis F V f

Spherical Mirrors The focal point (f) is halfway between C and V f = R / 2 R = 2f

Concave (converging) Mirror Images will form along the focal plane from incoming rays not parallel to the principal plane. Inside surface of the mirror forms a “cave”

Convex/Diverging Mirror Incoming rays that are parallel to the principal axis are reflected such that they appear to diverge from the focal point. This gives the viewer an expanded field of view.

Ray Diagrams The first ray is drawn parallel to the principal axis and is reflected through the focal point (F). The second ray is drawn through the center of curvature (C), to the mirror surface, and is reflected directly back. The intersection of these two rays is the position of the image.

Ray Diagrams – Concave Mirror C < Do Center of Curvature < Object Distance Real image is inverted (upside down) and smaller Ray 1 “ focuses” in on the focal point, F, after hitting the mirror.

Ray Diagrams – Concave Mirror F < Do < C Focal Point < Object Distance < Center of Curvature Real image is inverted (upside down) and larger

Do < F Object Distance < Focal Point Virtual image is not inverted (right side up) and larger Ray Diagrams – Concave Mirror

Image Characteristics The characteristics of the images can be described in the following manner: An image may be real or virtual An image may be upright or inverted An image may be larger or smaller than the object Section 7.3

Image Characteristics Real image – an image for which the light rays converge so that an image can be formed on a screen Real images form in front of the mirror where a screen can be positioned Virtual image – an image for which the light rays diverge and cannot form on a screen Virtual images form behind or inside the mirror where the light rays appear to converge A virtual image results when the object is inside the focal point

Ray Diagrams – Convex Mirror Always has virtual image that is not inverted (right side up) and smaller

Example – Concave Mirror An object is placed 25 cm in front of a concave mirror with a radius of curvature of 20 cm. Construct the ray diagram. Given: C = 20 cm, therefore f = 10 cm Image Characteristics: Real image, Inverted, Reduced Image Distance: approximately 17 cm 17 cm

Example – Concave Mirror An object is placed 15 cm in front of the concave mirror with a radius of curvature of 20 cm. Construct the ray diagram. Given: C = 20 cm, therefore f = 10 cm Image Characteristics: Real image, Inverted, Magnified Image Distance: approximately 30 cm 30 cm

Lenses A converging lens is thicker in the middle than at its rim and brings parallel light to a single point at a distance called the focal length of the lens. A diverging lens is thinner in the middle than at its rim and spreads out parallel light so that it seems to come from a point behind the lens.

Converging Spherical Lens Rays parallel to the principal axis converge at the focal point on the opposite side of the lens

Ray Diagrams The first ray is drawn parallel to the principal axis and then refracted by the lens through the focal point of the lens. The second ray is drawn through the center of the lens with no change in direction. The tip of the arrow occurs where these two rays intersect.

Converging Lens - Do > F If the object is beyond F, an inverted, real image is formed. The image becomes larger as F is approached. Object Outside the Focal Point Do > F

Converging Lens - Do < F Inside F, an object always forms a virtual image on the object side of the lens. Object Inside the Focal Point Do < F

Diverging Lens The Image is Always Upright and Smaller than Object

Example - Converging Lenses A convex lens has a focal length of 12 cm. Draw ray diagrams for an object at 18 cm from the lens. Image Characteristics: Real image, Inverted, Magnified Image Distance: approximately 36 cm 36 cm

Example - Diverging Lenses A convex lens has a focal length of 12 cm. Draw ray diagrams for an object at 8 cm from the lens. Image Characteristics: Virtual image, Upright, Magnified Image Distance: approximately 24 cm 24 cm

How a Camera Works A camera uses a converging lens to focus light rays from an object onto the film.

The Eye The human eye operates much like a camera The lens focuses the object on the retina. The image is reduced and inverted. The brain translates the information. Rods for night vision. Cones for color.

The Eye Farsightedness occurs when the eyeball is too short or lens of eye is too thin, focusing the object behind the retina and making it difficult to focus on nearby objects. Nearsightedness occurs when the eyeball is too long or lens of eye is too thick, focusing the object in front of the retina and making it difficult to focus on distant objects. Lasers can shave some of the lens off to correct it. converging lens (thicker in middle) diverging lens (thicker at edges) Farsighted Nearsighted Normal

The Eye Muscles in the eye change the thickness of the lens so we can focus on objects at different distances. As a person grows older the lens of the eye becomes less deformable and therefore cannot focus as readily. Reading glasses may be required.

Polarization Light is usually randomly polarized. Polaroid sunglasses can reduce certain orientations.

Polarization Light reflection from the surface of the ground or water is partially polarized in the horizontal direction. These polarized reflections increase the intensity and are seen as an annoying/dangerous “glare.” Polarizing sunglasses are oriented vertically and therefore do not allow the horizontal component of light to pass and thereby significantly reduce glare.

Summary Reflection θ r = θ i Refraction n = c / c m Spherical Mirrorsf = R / 2 Convex (diverging) or Concave (converging) expanded field Lenses Convex (converging) or Concave (diverging) thick at center thick at edge

Which of the following is true for a concave lens? (a) a lens that forms virtual images for D o > f. (b) a converging lens (c) a lens that forms real images for D o < f. (d) thicker at the center than at the edge.

Which is true for a real image? (a) It is formed behind a mirror. (b) It occurs only for D 1 = D o (c) It is always magnified. (d) It is formed by converging light rays.

Which is true for a virtual image? (a) It can be formed on a screen. (b) It is always formed by a convex lens. (c) It is formed on the object side of a lens. (d) It cannot be formed by a concave lens.

Which is true for a convex mirror? (a) It is a converging mirror. (b) It has a radius of curvature equal to f. (c) It forms magnified and reduced images. (d) It forms only virtual images.

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