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 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