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Lens Math

Lens Math

Learn how to use equations with lens math to determine information about the image like height and distance from the lens.

  • Click Here for a Worksheet with the Examples from this Page

Lens Math Variables

Name Variable Unit Unit Abbreviation
focal length f centimeters or meters cm or m
distance to image di centimeters or meters cm or m
distance to object do centimeters or meters cm or m
magnification M times x
height of image hi centimeters or meters cm or m
height of object ho centimeters or meters cm or m
Lens Math Equations

Virtual and Real Sides of a Lens

Light travels through a lens unlike a mirror which reflects.  Light travels to the real side given a positive (+) which is on the opposite side of the object.   If the image appears on the real side it will be given a positive value.  If the image appears on the virtual side, side of the object, it is virtual and given a negative symbol.

Lens Math Facts

  • For all lenses:
    • do is always positive + no matter what, an object is always real
  • For a concave lens:
    • (only produce, virtual, upright, reduced images)
    • f is always negative (-)
      • concave lens focal distances will be negative during math since the curve of the front side is toward the virtual side.
    • di is always negative (-)
      • because concave lenses only produce virtual upright images
Concave Lens Variable Signs
  • For a convex lens:
    • f is always positive (+)
    • convex lens focal distances will be positive since the curve of the front side is toward the real side.
    • di can be positive or negative.  You will determine this by the solution for di.
      • If di is a positive in your solution, the image is real and inverted.
      • If di is a negative in your solution, the image is virtual and upright.
Convex Lens Variable Signs

Lens Equation Tips

Lens Equation

do

  • First of all the object is always real and do will always be positive, never make this negative and if a solution is negative, you did something wrong.

di

  • If a problem says you have a virtual image, make the di negative.  If a problem says that the image appears on the same side as the object, make the di negative.
  • A real image is always inverted, a virtual image is always upright.

f

  • If you have a concave lens the f will always be negative
  • If you have a convex lens the f will always be positive
Rearranged Lens Equations

Magnification Equation

This equation can be used three ways

  • (hi / ho ) = (di / -do )
  • M= hi / ho
  • M= -di / do

M

  • you can solve for M with hi and ho
    • M= hi / ho
  • you can solve for M with di and do
    • M= -di / do
  • If M is 1 the image is not magnified
  • If M is less than 1 the image is reduced
  • If M is greater than 1 the image is enlarged
  • If M is negative the image is real and inverted
  • If M is positive the image is virtual and upright

Example Problems

Use the video provided for extra support through these questions.

1. An object is 5.00 meters away from a convex lens, which produces a real image 1.00 meters away.  What is the focal length of the lens?

1

2. An object is 5.00 meters away from a convex lens, which produces a real image 1.00 meters away.  What is the magnification of the image?

2

3. An object is 6.0 centimeters away from a convex lens, which produces a virtual image 7.0 centimeters away.  What is the focal length of the lens?

3

4. A 2 cm tall object is 6.0 centimeters away from a convex lens, which produces a virtual image 7.0 centimeters away.  What is the height of the image?

4

5. An 8 cm tall object is 12.0 centimeters away from a concave lens, which produces a virtual image 7.0 centimeters away.  What is the focal length of the lens?

5

6. An 8 cm tall object is 12.0 centimeters away from a concave lens, which produces a virtual image 7.0 centimeters away.  What is the height of the image?

6

7. Find the image distance for a convex lens with an object distance of 15 cm and a focal length of 30 cm.

7

8. Given di = -18 cm, do= 6 cm, and M=3, describe the image.

8

9. Find the focal length for a convex lens with an object distance of 60 cm and an real image distance of 15 cm.

9

10. Find the distance an object is away from a convex lens with an real image formed 60 cm away and a focal length of 20 cm.

10

PhET Lens Lab

Return to the previous section by clicking here to complete a PhET lens lab that includes lens math.

  • PhET Lens Lab

Links

  • Back to the Main Electromagnetic Waves Page
  • Back to the Stickman Physics Home Page
  • Equation Sheet

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Unit 1: One Dimensional Motion
Unit 2: 2D Motion
Unit 3: Newton’s Laws and Force
Unit 4: Universal Gravitation and Circular Motion
Unit 5: Work, Power, Mechanical Advantage, and Simple Machines
Unit 6: Momentum, Impulse, and Conservation of Momentum
Unit 7: Electrostatics
Unit 8: Current and Circuits
Unit 9: Magnetism and Electromagnetism
Unit 10: Intro to Waves
Unit 11: Electromagnetic Waves
Unit 12: Nuclear Physics

AP Physics 1 Pages (Deeper Dive into Concepts)

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