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length fof a camera is the distance required for the lens to converge light to a single gle of view a of a camera describes the angular range (either horizontally, vertically, is imaged by a camera. Object Lens where d is the dimension of the image sensor or film. 2f = 2arctan- nm camera has image dimensions of 24 mm (vertically) by 36 mm (horizontally). If h is 50 mm, find the vertical and horizontal viewing angles. Round to the nearest ree.

length fof a camera is the distance required for the lens to converge light to a single gle of view a of a camera describes the angular range (either horizontally, vertically, is imaged by a camera. Object Lens where d is the dimension of the image sensor or film. 2f = 2arctan- nm camera has image dimensions of 24 mm (vertically) by 36 mm (horizontally). If h is 50 mm, find the vertical and horizontal viewing angles. Round to the nearest ree.

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**Problem 1: Show your work.** The effective focal length, \( f \), of a camera is the distance required for the lens to converge light to a single focal point. The angle of view \( \alpha \) of a camera describes the angular range (either horizontally, vertically, or diagonally) that is imaged by a camera. **a.** Show that \( \alpha = 2 \arctan \frac{d}{2f} \) where \( d \) is the dimension of the image sensor or film. **b.** A typical 35-mm camera has image dimensions of 24 mm (vertically) by 36 mm (horizontally). If the focal length is 50 mm, find the vertical and horizontal viewing angles. Round to the nearest tenth of a degree. **Diagram:** - The diagram illustrates a camera lens focusing light from an object to an image sensor or film. - The lens is marked at the center with lines indicating light paths that converge at the focal point. - The distance from the lens to the film is labeled \( f \), the focal length. - The dimension of the film is marked as \( d \). - The angle \( \alpha \), subtending the sensor or film from the focal point, is shown as \( \alpha/2 \) on each side of the central axis.
Transcribed Image Text:**Problem 1: Show your work.** The effective focal length, \( f \), of a camera is the distance required for the lens to converge light to a single focal point. The angle of view \( \alpha \) of a camera describes the angular range (either horizontally, vertically, or diagonally) that is imaged by a camera. **a.** Show that \( \alpha = 2 \arctan \frac{d}{2f} \) where \( d \) is the dimension of the image sensor or film. **b.** A typical 35-mm camera has image dimensions of 24 mm (vertically) by 36 mm (horizontally). If the focal length is 50 mm, find the vertical and horizontal viewing angles. Round to the nearest tenth of a degree. **Diagram:** - The diagram illustrates a camera lens focusing light from an object to an image sensor or film. - The lens is marked at the center with lines indicating light paths that converge at the focal point. - The distance from the lens to the film is labeled \( f \), the focal length. - The dimension of the film is marked as \( d \). - The angle \( \alpha \), subtending the sensor or film from the focal point, is shown as \( \alpha/2 \) on each side of the central axis.
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