## Focal Lengths

### Materials

• Lens and lens stand
• Cardstock paper
• Paper clip
• Sticker in the shape of a letter
• Mini flashlight
• Meter stick or measuring tape

### Directions

1. Place your lens at the 70cm mark of your meter stick (have someone hold it if you don’t have a lens stand)
2. Place your Cardstock at the 100 cm mark of your meter stick (either have someone hold it up or find a way to tape it up)
3. Put your sticker on the lens of your mini flashlight. Then hold your lens directly behind the lens and the cardstock. If all three don’t line up, move them so they do.
4. Move your flashlight either forward or backwards until a clear image of your letter shows up on the cardstock
5. Measure how far you are from your lens.
6. Place your Cardstock in a different location and repeat.

### Explanation

To see a clear image on the opposite side of a lens, the distance between your eye and the lens must be proportional to distance between the lens and the object. If you put your light bulb too close or too far away from the lens, the image would be very blurry and unclear. When the image is at its clearest, the distance between the light and the lens is called the object distance while the distance between the lens and the image (or the cardstock) is called the image distance.

Each lens has a focal point. A focal point is the point in space where parallel light rays meet after passing through the lens. They are also proportional to the image and object distance. The equation used to find the focal length is  where f is the focal length, d_i is the image distance, and d_o is the object distance. No matter how your image distance and object distance change, your lens will always have the same focal length. Try to use your measurements to calculate the focal length.