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Magnifying Power and Focal Length of a Lens

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Author: Erin Bjornsson

A lens is a clear object, usually made of glass or plastic, which is used to refract, or bend light. Lenses can concentrate light rays (bring them together) or spread them out. Common examples of lenses include camera lenses, telescope lenses, eyeglasses, and magnifying glasses. Lenses are often double lenses, meaning they have two curved sides. A convex lens is rounded outward, while a concave lens curves inward. (A great way to remember this is that a concave lens creates an indent like a cave!)

The center axis through a lens is called the principal axis. On lenses that concentrate light rays, the point at which the rays meet, the focal point, is located on the principal axis. The distance the focal point is from the surface of a lens is called the focal length of a lens, and is important when determining the magnifying power of devices like magnifying glasses.

Magnifying power is how much larger a given lens can make an image appear. This is a direct relationship between the focal length of the lens and the least distance of distinct vision, or LDDV. The LDDV is the closest your eyes can comfortably look at an object.

Objective: Which magnifying glass is the most powerful?

Materials

  • Magnifying glasses of different sizes or powers
  • Wall
  • Flashlight
  • Meter stick
  • Stuff to magnify!

Procedure

  1. For each magnifying glass, stand close to a wall and shine the flashlight through each magnifying glass onto the wall.
  2. Move the flashlight closer to or farther away from the wall until the light refracts to a single point.
  3. Measure the distance from the lens to the wall to get a reading (in centimeters) to find the focal length. It can be handy to have a friend help you here.
  4. Create a table to manage your data.
  5. Now, choose a small object. Bring the object as close to your eyes as you can before it becomes blurry and out of focus.
  6. Measure and record this distance. This is the Least Distance of Distinct Vision, or LDDV.
  7. Calculate the magnifying power of each magnifying lens. Use the following formula.

Focal Length Equation

Where Mp is Magnifying power, LDDV is the least distance of distinct vision you found in step 7, and Lf is the focal length of the lens.

  1. Test it out! Do your observations match up with each calculated magnifying power? Take a look at how the same object looks under different magnifying glasses to compare.

Results

The distance of distinct vision is usually somewhere around 10 cm for a person with perfect vision. Magnifying lenses with shorter focal lengths will have greater magnifying power.

Why?

Magnifying power is inversely related to the focal length of a lens: the bigger the focal length, the lower the magnifying power. The LDDV is a constant number, as it usually tends to be the same for people with good vision. Focal length and LDDV have to be measured in the same units for the calculations to work out—they’re usually measured in meters (or centimeters).

Another feature of lenses is called lens power, very similar to magnifying power, and is expressed in the following relationship:

Lens Power Equation

The units of focal length Lf are meters. Lens power is therefore measured in 1/m, also called diopters.

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