Magnification and Mirror Equations

» We have discovered the characteristics [LA(O)ST] of images in mirrors using ray diagram rules. You can also predict the characteristics of an image using two equations.

1. MIRROR/LENS EQUATION

f = focal lengthdi = distance from mirror to imagedo = distance from mirror to object

1 = 1 + 1

f di do

1 = 1 + 1

f di do

The image distance, di, is negative if the image is virtual (behind the mirror/infront of the lens).

» Magnification: the change in image size as compared to the object

M = hi or M = - di or hi = - di

ho do ho do

M = hi or M = - di or hi = - di

ho do ho do

hi = height of imageho = height of object-di = distance of image from the mirror/lensdo = distance of object from the mirror/lens

2. MAGNIFICATION EQUATIONS

• The image height, hi, is negative if the image is inverted relative to the object.

• If the image size is greater than the object, then the magnification will be greater than 1.

• If the image size is smaller than the object, then the magnification will be smaller than 1.

Example Problems» Example Problem #1 [Use G.U.E.S.S.]» A microscope produces an image that is 5.50 × 10–4 m high

from an object that is 2.00 × 10–6 m high. What is the magnification of this microscope?

» Given: hi = 5.50 × 10–4 m, ho = 2.00 × 10–6 m » Unknown: Magnification» Equation: M = hi

ho

» Substitute: M = 5.50 × 10–4 m 2.00 × 10–6 m

» Statement: The magnification of the microscope is 275 x.

» Example Problem #2» A concave mirror has a focal length of 12 cm. An object with

a height of 2.5 cm is placed 40.0 cm in front of the mirror.a. Calculate the image distance.b. Calculate the image height

» Given: f = 12 cm ho = 2.5 cm do = 40.0 cm

» Unknown: di hi

» Equation: 1/f = 1/di + 1/do

» Substitution:

» Statement: The distance to the image is 17 cm and the image is 1.1 cm high.

» EXAMPLE PROBLEM #2 - CHECK YOUR WORK

» Draw a ray diagram to verify your solution.» NOTE: C is twice the value of F.» C = 2 X 12 cm = 24 cm. The object is at 40 cm, so it is beyond C.» Therefore, the image should be closer to the mirror than the object,

smaller than the object, and inverted.

More PracticePRACTICE: On a separate sheet, complete the questions using the GUESS method.

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4. In the diagram below, the object is beyond C. Use the data in the diagram to answer the questions below.

a. Calculate the image distance.b. Calculate the image height.

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5. A dancer is applying make-up using a concave mirror. The dancer’s face is 35 cm in front of the mirror, and the image is 72 cm behind the mirror. Use the mirror equation to calculate the focal length of the mirror.

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6. A convex mirror has a focal length of 0.9 m. An object with a height of 0.40 m is 2.5 m from the mirror.a. Calculate the image distance.b. Calculate the image height.

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» Video of effects of concave mirrors:concave mirror focal point