PhysicsLAB: Thin Lens Equation

The thin lens equation is stated as follows:

where

d_o is the distance (measured along the axis) from the object to the center of the lens
d_i is the distance (measured along the axis) from the image to the center of the lens
f is the focal length of the lens

The expression 1/f in called the power of a lens. It is measured in Diopters, where 1 D = 1 m^-1.

When using this equation, signs are very important:

d_o	positive	when the object is placed "in front of the lens"

d_i	positive	when real images are formed (inverted, "behind the lens")
d_i	negative	when virtual images are formed (upright, "in front of the lens")

f	positive	when the lens is converging
f	negative	when the lens is diverging

Remember that d_o, d_i, and f must be measured in the same unit - usually meters is preferred.

The following formula is used to calculate the magnification of an image:

If a problem states that a real image is formed that is twice as large as an object, then you would use the relationship d_i = +2d_o in the thin lens equation. If a problem states that a virtual image is formed that is twice as large as the object, then you would use the relationship that d_i = −2d_o.

Refer to the following information for the next three questions.

Suppose you are initially given a converging lens, made from crown glass, that has a focal length of +0.10 meter.

	If this lens is to be used in air, which cross-sectional figure best represents its shape?

	An object is placed 0.30 meter from the lens in the previous question. How far from the lens will the image of this object be formed?

	Suppose this 0.800-meter tall object is now placed 0.20 meter in front of a second converging lens. If the distance of the image from the lens is 0.40 meter, then the height of the image is

Refer to the following information for the next four questions.

Suppose you are now given a double concave lens, also made from crown glass, that has a focal length of −0.10 meter.

	Which cross-sectional figure best represents its shape?

	This diverging lens can form only form ____ images.

	An object is placed 0.20 meter from this diverging lens. How far from the lens will the image of the object be formed?

	If the object in the previous question was 4.5 centimeters tall, how tall is its image?