UNIT 8 Light and Optics

ConcepTest 35.2b Mirror II 1) same as your height 2) less than your full height but more than half your height 3) half your height 4) less than half your height 5) any size will do You stand in front of a mirror. How tall does the mirror have to be so that you can see yourself entirely?

ConcepTest 35.2b Mirror II 1) same as your height 2) less than your full height but more than half your height 3) half your height 4) less than half your height 5) any size will do You stand in front of a mirror. How tall does the mirror have to be so that you can see yourself entirely? Trace the light rays from the image’s foot to the mirror and then to the eye. Since we know that qi = qr , you need a mirror only half your size.

ConcepTest 35.2c Mirror III 1) No. 2) Yes. 3) Depends on the mirror. 4) Depends on the person. Does this depend on your distance from the mirror?

ConcepTest 35.2c Mirror III 1) No. 2) Yes. 3) Depends on the mirror. 4) Depends on the person. Does this depend on your distance from the mirror? The further you step back, the smaller the incident and reflected angles will be. But the rays will still be reflected at the same points, so the ray from the foot will still be reflected at mid-height.

Thursday February 16th Light and Optics

TODAY’S AGENDA UPCOMING… Curved Mirrors Concave Thursday, February 16 TODAY’S AGENDA Curved Mirrors Concave Hw: Practice B (all) p462 UPCOMING… Fri: NO School Mon: Curved Mirrors Convex Tue: Problem Quiz #1 Color and Polarization Wed: Refraction

Chapter 13 Light and Reflection

Formation of Images by Spherical Mirrors Spherical mirrors are shaped like sections of a sphere, and may be reflective on either the inside (concave) or outside (convex).

Formation of Images by Spherical Mirrors Rays coming from a faraway object are effectively parallel.

Formation of Images by Spherical Mirrors Parallel rays striking a spherical mirror do not all converge at exactly the same place if the curvature of the mirror is large; this is called spherical aberration.

Formation of Images by Spherical Mirrors If the curvature is small, the focus is much more precise; the focal point is where the rays converge.

Formation of Images by Spherical Mirrors Using geometry, we find that the focal length is half the radius of curvature: Spherical aberration can be avoided by using a parabolic reflector; these are more difficult and expensive to make, and so are used only when necessary, such as in research telescopes.

Formation of Images by Spherical Mirrors We use ray diagrams to determine where an image will be. For mirrors, we use three key rays, all of which begin on the object: A ray parallel to the principal axis; after reflection it passes through the focal point. 2. A ray through the focal point; after reflection it is parallel to the principal axis. 3. A ray through the focal point; after reflection it is parallel to the principal axis.

Images Formed by Spherical Mirrors Concave Mirror C center of curvature = R R = radius C Principle Focal Point

Images Formed by Spherical Mirrors Image Characteristics Type: Real or Virtual Size: Larger, Smaller, or Same (as the Object) Orientation: Upright or Inverted do: always positive di: real is positive; virtual is negative f: In front of mirror is positive; Behind mirror is negative

Images Formed by Spherical Mirrors Concave Mirror Image Characteristics Case #1 parallel ray real smaller inverted focal ray central ray image image found between C and f

Images Formed by Spherical Mirrors Concave Mirror Image Characteristics Case #2 real same inverted image image found at the C

Images Formed by Spherical Mirrors Concave Mirror Image Characteristics Case #3 real larger inverted C image image found beyond C

Images Formed by Spherical Mirrors Concave Mirror Vampire case Image Characteristics Case #4 No image C

Images Formed by Spherical Mirrors Make-up case Concave Mirror Case #5 image C Image Characteristics virtual larger upright image found behind mirror

Images Formed by Spherical Mirrors Concave Mirror Light Source at the Focal Point Produces Parallel Rays of Light

Images Formed by Spherical Mirrors Concave Mirror do di f ho hi h i h o = d i −f f

Images Formed by Spherical Mirrors Concave Mirror do di f ho hi

Images Formed by Spherical Mirrors h i h o = d i d o → d o d i −f =f d i d o d i − fd o =f d i → d o d i =f d i + fd o

Images Formed by Spherical Mirrors d o d i =f d i + d o → d i d o d i + d o d o d i = 1 f

Images Formed by Spherical Mirrors Concave Mirror Virtual Image f

Images Formed by Spherical Mirrors Concave Mirror do f ho hi di h i h o = d i +f f

Images Formed by Spherical Mirrors ho hi do di Concave Mirror Magnification M > 1 Larger M < 1 Smaller M + Upright M - Inverted M = 1 Same M =

Images Formed by Spherical Mirrors A object is placed between a concave mirror and its focal point. The image formed is (A) virtual and inverted. (B) virtual and upright. (C) real and upright. (D) real and inverted.

Images Formed by Spherical Mirrors (Problem) A mirror at an amusement park shows an upright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius of curvature? M = The image characteristics identify the case as concave #5 (larger, virtual, and upright). 3 = = di = -4.2 m

Images Formed by Spherical Mirrors If you stand in front of a concave mirror, exactly at its focal point, (A) you will see your image at your same height. (B) you won't see your image because there is none. (B) you will see your image, and you will appear smaller. (C) you will see your image and you will appear larger.

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