Mirrors

Outline Vocabulary Law of Reflection Ray Diagrams Images from a Concave Mirror Virtual vs Real Mirrors Mirror Equation

Vocabulary Principal axis- a line passing through the center of a virtual sphere (on which the mirror sits) and the exact center of a mirror

Vocabulary Center of Curvature- The point in the center of the sphere from which the mirror was sliced (C)

Vocabulary Vertex- the point on the mirror’s surface where the principal axis meets the mirror (A)

Vocabulary Focal Point- point half way between the vertex and the center of curvature (F)

Vocabulary Radius of Curvature- distance from the vertex to the center of curvature (R)

Vocabulary Focal Length- distance from the vertex to the focal point (f)

Law of Reflection For a light ray reflected off the surface of any mirror, the angle of incidence equals the angle of reflection, where both angles are measured from the surface normal 𝜃 𝑖 = 𝜃 𝑟

Law of Reflection For a concave mirror: Normal line extends from point of incidence to center of curvature Angle of incidence is measured from this normal

Law of Reflection Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection. Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection.

Law of Reflection For a convex mirror: Normal line is perpendicular to a tangent line at point of incidence Angle of incidence is measured from this normal

Ray Diagrams Incident rays connect object to mirror Reflected rays obey the law of reflection Angle of incidence = angle of reflection Measured from normal at point of incidence Image is produced at intersection of reflected rays

Drawing Ray Diagrams Draw 2 rays from the top of the object to the mirror One ray must run parallel to the radius of curvature One ray must run from the object, through the focal point

Drawing Ray Diagrams Apply the law of reflection to each incident ray Repeat, starting at bottom of object

Drawing Ray Diagrams

Images from Concave Mirrors Case 1: Object is located beyond center of curvature Image is inverted Image is smaller than object Image is located between C and F Magnification is less than 1 Image is real

Images from Concave Mirrors Case 2: Object is located at center of curvature Image is inverted Image is same size as object Image is located at C Magnification is 1 Image is real

Images from Concave Mirrors Case 3: Object is located between center of curvature and focal point Image is inverted Image is larger than object Image is located beyond C Magnification is greater than 1 Image is real

Images from Concave Mirrors Case 4: Object is located at focal point No image is formed

Images from Concave Mirrors Case 5: Object is located in front of focal point Image is upright Image is larger than object Image is located beyond mirror Magnification is greater than 1 Image is virtual

Virtual vs. Real Images Virtual Images Real Images Formed in locations where light does not actually reach Light only appears to emanate from that location A surface placed at the image location will not show the image Image is located beyond mirror Light does actually converge A surface placed at the convergence location will show the image

Mirror Equation 1 𝑓 = 1 𝑑 𝑜 + 1 𝑑 𝑖 f = focal length do = distance between mirror and object di = distance between mirror and image

Magnification Ratio of height of image to height of object 𝑀= ℎ 𝑖 ℎ 0 𝑀= ℎ 𝑖 ℎ 0 𝑀=− 𝑑 𝑖 𝑑 𝑜

Sign Conventions for Mirror Equations Variable Positive Negative f Concave mirror Convex mirror di Real image, located on object’s side of mirror Virtual image, located behind mirror hi Upright image, virtual Inverted image, real

Clicker Question 1 A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. What is the image distance? 15.18 cm 22.73 cm 30.51 cm 45.73 cm B

Clicker Question 2 A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. What is the image height? 5.98 cm 4.00 cm 8.03 cm 12.03 cm A

Clicker Question 3 A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. Will the image be upright or inverted? Upright Inverted B

Clicker Question 4 A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. Is the image real or virtual? Real Virtual A

Clicker Question 5 A 4.0-cm tall light bulb is placed a distance of 8.3 cm from a concave mirror having a focal length of 15.2 cm. What is the image distance? -18.28 cm -0.14 cm 0.14 cm 18.28 cm (NOTE: this is the same object and the same mirror, only this time the object is placed closer to the mirror.) D

Clicker Question 6 A 4.0-cm tall light bulb is placed a distance of 8.3 cm from a concave mirror having a focal length of 15.2 cm. What is the image height? 2.31 cm 6.9 cm 8.81 cm 60.8 cm C

Clicker Question 7 A 4.0-cm tall light bulb is placed a distance of 8.3 cm from a concave mirror having a focal length of 15.2 cm. Is the image upright or inverted? Upright Inverted A

Clicker Question 8 A 4.0-cm tall light bulb is placed a distance of 8.3 cm from a concave mirror having a focal length of 15.2 cm. Is the image real or virtual? Real Virtual B

Practice Problem 1 A spherical concave mirror has a radius of curvature of +62 cm. What is the focal length of the mirror?

Practice Problem 2 Every morning Bob Gillette uses a shaving mirror with a focal length of 72 cm to view the image of his face. Supposing his face is 18 cm from the mirror, determine the image distance and the magnification of his face.

Practice Problem 3 The infamous Chinese magician Foo Ling Yu places a 56-mm tall light bulb a distance of 124 cm from a spherical concave mirror with a focal length of 62 cm.

Practice Problem 4 In a physics demonstration, a concave mirror having a 50.0 cm focal length is used to create images of a candle located at various locations along its principal axis. Beginning from a distance of several meters from the mirror, a candle is moved forward and its image is projected onto an opaque screen. Determine the image distances (distance from mirror to image) for object distances (distance from object to mirror) of … a. … 125.0 cm b. … 100.0 cm c. … 75.0 cm d. … 50.0 cm (Be careful with your math; the result is surprising.) e. … 25.0 cm