How is the focal length of a convex lens calculated?

The focal length of a convex lens is calculated using the formula ( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} ). This formula is derived from the lens maker's equation and takes into account both the object distance (the distance from the lens to the object) and the image distance (the distance from the lens to the image).

This relationship shows that the focal length ( f ) is dependent on how far the object is placed from the lens and where the image is formed. When substituting the known values of ( d_o ) and ( d_i ) into this equation, one can accurately find the focal length of the lens, allowing for calculations related to image formation and location.

The correct usage of this formula is crucial in optics as it helps to understand how lenses focus light and form images, which is foundational knowledge in the study of optics.