A statue is 6.6 m from the opening of a pinhole camera, and...

A statue is $6.6 \mathrm{~m}$ from the opening of a pinhole camera, and the screen is $2.8 \mathrm{~m}$ from the pinhole. (a) Is the image erect or inverted? (b) What is the magnification of the image? (c) To get a brighter image, we enlarge the pinhole to let more light through, but then the image looks blurry. Why? (d) To admit more light and still have a sharp image, we replace the pinhole with a lens. Should it be a converging or diverging lens? Why? (e) What should the focal length of the lens be?

Key Concepts

Pinhole Camera Principle

A pinhole camera forms an image by allowing light rays from an object to pass through a small aperture (the pinhole) and project an inverted image onto a surface (the screen). Because the rays cross at the pinhole, the resulting image is upside down relative to the original object.

Image Magnification

Magnification in a camera setup is determined by the ratio of the distance from the aperture to the screen (image distance) over the distance from the object to the aperture (object distance). This ratio indicates how much larger or smaller the image is compared to the object and includes the inversion characteristic of pinhole projection.

Aperture Size and Image Sharpness

There is a trade-off associated with the size of the pinhole (aperture). A very small pinhole results in a sharp but dim image because it restricts the amount of light entering the camera. Enlarging the pinhole increases the light and brightness of the image but allows rays from different parts of the object to overlap, causing blurriness due to a decrease in depth of focus.

Converging Lenses and Focusing

Replacing the pinhole with a lens addresses the trade-off between brightness and sharpness. A converging lens (convex lens) can focus parallel or diverging light rays to form a real, sharp image on the screen. This is because a converging lens refracts light rays so that they meet at a focal point, allowing for a brighter image without the blurring associated with an oversized aperture.

Lens Formula and Focal Length

The lens formula, given by 1/f = 1/object_distance + 1/image_distance, relates the focal length of a lens to the distances of the object and the image from the lens. This relation helps determine the appropriate focal length needed to produce a sharp image on the screen when the object distance and image distance are known.

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