The focal length of a lens or mirror can be calculated using a specific formula that relates object distance, image distance, and focal length.
Understanding Focal Length
Focal length is a crucial property of lenses and mirrors. It determines how strongly the system converges or diverges light. A shorter focal length indicates a stronger convergence or divergence.
The Formula
The fundamental formula to calculate focal length is:
1/do + 1/di = 1/f
Where:
- do = object distance (distance from the object to the lens or mirror)
- di = image distance (distance from the image to the lens or mirror)
- f = focal length
Applying the Formula: Step-by-Step
- Identify the known values: Determine the object distance (do) and the image distance (di). Make sure both are in the same units (e.g., centimeters, meters).
- Substitute the values into the formula: Plug the known values of 'do' and 'di' into the equation 1/do + 1/di = 1/f.
- Solve for 'f':
- Find a common denominator for 1/do and 1/di, and add the two fractions.
- Take the reciprocal of the result to find the value of 'f' (focal length).
Example
Let's say an object is placed 30 cm (do = 30 cm) from a lens, and a clear image is formed 15 cm (di = 15 cm) on the other side of the lens. What is the focal length?
- Known values: do = 30 cm, di = 15 cm
- Substitution: 1/30 + 1/15 = 1/f
- Solve:
- 1/30 + 2/30 = 1/f
- 3/30 = 1/f
- 1/10 = 1/f
- f = 10 cm
Therefore, the focal length of the lens is 10 cm.
Important Considerations
- Sign Conventions: Be mindful of sign conventions, especially for lenses and mirrors. Distances are usually positive when on the same side of the lens or mirror as the observer and negative when on the opposite side. This is particularly relevant for di.
- Units: Ensure all distances are in the same units to obtain the correct focal length value.
- Thin Lens Approximation: This formula works best for thin lenses. For thick lenses, more complex calculations are necessary.
