Solving the Equation: 1/f = 1/do + 1/di
In optics, the equation 1/f = 1/do + 1/di is a fundamental concept in understanding the relationship between the focal length of a lens, the object distance, and the image distance. In this article, we will solve for do (object distance) and explain the steps involved in the process.
The Equation: 1/f = 1/do + 1/di
The equation 1/f = 1/do + 1/di is known as the lens equation or the Gaussian lens equation. It relates the focal length (f) of a lens to the object distance (do) and the image distance (di).
Solving for do (Object Distance)
To solve for do, we need to rearrange the equation to isolate do on one side. Here are the steps:
Step 1:
Rearrange the equation to get rid of the fractions:
1/f = 1/do + 1/di
Multiply both sides by fdo to eliminate the fractions:
do = fdo/di + f
Step 2:
Subtract f from both sides to isolate do:
do - f = fdo/di
Step 3:
Divide both sides by (1 - f/di) to solve for do:
do = f / (1 - f/di)
Therefore, the object distance (do) can be expressed in terms of the focal length (f) and the image distance (di).
Conclusion
In this article, we have successfully solved the equation 1/f = 1/do + 1/di for do (object distance). The resulting equation, do = f / (1 - f/di), shows that the object distance is a function of the focal length and the image distance. This equation is a fundamental concept in optics and is widely used in the design and analysis of optical systems.
