A camera uses a lens with a focal length of 0.0500 m and can...

A camera uses a lens with a focal length of 0.0500 m and can take clear pictures of objects no closer to the lens than 0.500 m. For closer objects the camera records only blurred images. However, the camera could be used to record a clear image of an object located 0.200 m from the lens, if the distance between the image sensor and the lens were increased. By how much would this distance need to be increased?

Key Concepts

Thin Lens Equation

The thin lens equation, given by 1/f = 1/d? + 1/d?, relates the focal length of a lens (f) to the distances of the object (d?) and the image (d?). This fundamental relation is used to determine where an image will form and is essential in applications such as photography to ensure that the image sensor is correctly positioned for sharp focus.

Focal Length

Focal length is an inherent property of a lens that measures the distance over which initially parallel rays of light are brought to a focus. It determines the magnification of the image and how the lens converges or diverges light, playing a critical role in calculating the needed image sensor placement.

Object Distance

Object distance is the measure of the distance between the object being imaged and the lens. Its value is crucial in the thin lens equation because it directly affects where the image is formed as well as the overall clarity and geometry of the image.

Image Distance

Image distance refers to the distance from the lens to the point where the image is in focus, such as the sensor in a camera. Accurately determining or adjusting this distance based on the object distance and focal length is key to achieving a sharp image.

Focus Adjustment

Focus adjustment entails modifying the position of the image sensor relative to the lens so that the image formed by the lens is sharp. This process is guided by the thin lens equation, ensuring that the sensor is placed at the correct image distance for a given object distance and focal length.

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