1. What is the Lens Formula?

The lens formula is a fundamental equation in optics that relates the focal length of a lens to the distances of the object and the image from the lens. It is expressed as:

Where:

• \( f \) — Focal length of the lens
• \( d_o \) — Object distance from the lens
• \( d_i \) — Image distance from the lens

2. How Does the Calculator Work?

The calculator uses the lens formula to calculate the image distance when given the focal length and object distance:

Explanation: The formula calculates where an image will form based on the object position and the lens's focal length. For convex lenses, the focal length is positive.

3. Importance of Lens Formula

Details: Understanding the lens formula is crucial for designing optical systems, including cameras, microscopes, telescopes, and eyeglasses. It helps predict image formation characteristics.

4. Using the Calculator

Tips: Enter focal length and object distance in centimeters. Both values must be positive numbers. The calculator will compute the corresponding image distance.

5. Frequently Asked Questions (FAQ)

Q1: What happens when the object is at the focal point?
A: When d_o = f, the denominator becomes zero, making the image distance undefined. In practice, the image forms at infinity.

Q2: What does a negative image distance mean?
A: A negative image distance indicates a virtual image formed on the same side of the lens as the object.

Q3: How does this apply to concave lenses?
A: For concave lenses, the focal length is negative, and the formula works the same way but produces different image characteristics.

Q4: What are the sign conventions for lens formula?
A: For convex lenses: f is positive, d_o is positive for real objects. d_i is positive for real images and negative for virtual images.

Q5: Can this formula be used for thick lenses?
A: The formula is most accurate for thin lenses. For thick lenses, additional factors need to be considered.