Ch 31: Geometric OpticsSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Mirror Equation

Example #1: Object in Front of Convex Mirror

Practice: A 4 cm tall object is placed in 15 cm front of a concave mirror with a focal length of 5 cm. Where is the image produced? Is this image real or virtual? Is it upright or inverted? What is the height of the image?

Practice: You want to produce a mirror that can produce an upright image that would be twice as tall as the object when placed 5 cm in front of it. What shape should this mirror be? What radius of curvature should the mirror have?

Additional Problems
An upright object that is 2.0 mm tall is placed to the left of a concave spherical mirror that has focal length f = +20.0 cm. The image is 4.0 mm tall and is upright. Is the image real or virtual? A. Real B. Virtual
Which of the following best describes the image of a concave mirror when the object distance is equal to the radius of curvature? a. virtual, upright and magnification one b. real, inverted and magnification less than one c. virtual, upright and magnification less than one d. real, inverted and magnification one
 An object is placed 6.0 cm to the left of a concave mirror. The image formed by the mirror is 8.0 cm to the right of the mirror. The image is (a) real and inverted (b) real and upright (c) virtual and inverted (d) virtual and upright
An object 6.0 mm tall is placed 0.45 m to the left of a spherical mirror. The image formed by the mirror is inverted and is 2.0 mm tall. What is the focal length of the mirror? Be sure to indicate whether the focal length is positive or negative.
You want to design a mirror for viewing erect images of objects. The image should have a magnification of 0.5 when the mirror is 2.0 m from an object. Find the shape and radius of curvature of the mirror.
Suppose you wanted to start a fire using sunlight and a mirror. Which of the following statements is most accurate? a) It would be best to use a plane mirror. b) It would be best to use a convex mirror. c) It would be best to use a concave mirror, with the object to be ignited positioned halfway between the mirror and its center of curvature. d) It would be best to use a concave mirror, with the object to be ignited positioned at the center of curvature of the mirror. e) One cannot start a fire using a mirror, since mirrors form only virtual images.
A concave mirror is placed 0.800 m to the left of an object that is 2.00 mm tall. The mirror forms an image on a screen that is to the right of the object. The height of the image is 6.00 mm. What is the distance from the object to the screen?
An object located 125 cm from a concave mirror forms a real image 80 cm from the mirror. The mirror is then turned around so that its convex side faces the object, and is moved so that the image is now 40 cm behind the mirror. How far was the mirror moved? 1. 90.9091 2. 13.6957 3. 134.146 4. 97.2222 5. 70.0 6. 107.66 7. 164.434 8. 10.5263 9. 8.28829 10. 86.0377
An object with height y = 2 mm is placed a distance s = 24 cm in front of the vertex of a concave spherical mirror with radius of curvature R = 16 cm, as shown in the figure below. What are the image distance s' and the height y' of the resulting image? s' = _______________ y' = _______________
As you walk away from a plane mirror on a wall, your image A) is always a real image, no matter how far you are from the mirror. B) may or may not get smaller, depending on where the observer is positioned. C) changes from being a virtual image to a real image as you pass the focal point. D) gets smaller. E) is always the same size.
An erect object is 50 cm from a concave mirror of radius 60 cm. If the object is moved to a new position, such that the new lateral magnification is +2.5. The new object distance, in cm, is closest to:  A) 18 B) 24 C) 30 D) 36 E) 42
A production line inspector wants a mirror that produces an upright image with magnification of 6.6 when it is located 16.1 mm from a machine part. What kind of mirror would do this job? 1. convex mirror 2. Unable to determine. 3. concave mirror
An object is 17.9 cm from the surface of a reflective spherical Christmas-tree ornament 6.83 cm in radius. What is the apparent position of the image?