Curved Mirrors Chapter 13 Section 3

Mirror Terminology  Ccenter of curvature  Rradius of curvature

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)

Mirror Terminology  pobject distance  qimage distance

Mirror Terminology  hobject height  h’image height

Mirror Terminology  Inverted  Upright

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

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

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

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”

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)

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

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

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

#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?

#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

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

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

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

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

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

#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

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

#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