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Do I really "Gain a stop?" Locked

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Re: Do I really "Gain a stop?"

Sometimes we get lost in the minutia. Focal length determines the size of the image; the longer the focal length, the larger the image. The image of objects produced by a 100mm lens will be twice as larger as images produced by a 50mm lens.

Focal length is one key factor as to image brightness. The brightness of a the image produced by a 100mm lens will be four times dimmer than the image produced by a 50mm lens. This is because the larger image produced by the 100mm lens covers 4x more surface area. If the working diameters of the apertures are the same for both lenses than the difference in image brightness is changed by a factor of 4.

A focal reducer intercepts the converging rays of the leading lens. The focal reducer adds positive refractive power. The image forming rays are forced to bend inward (more refraction). The result is a shortening of the back-focus distance (lens to image plane). The shorter back-focus reduces the image size. The reduced magnification prompts a brighter image.

A key number in photo math is the square root of 2 = 1.414. We can round this number to 1.4 without losing too much accuracy. The f-number system is based on this value. A 2x change in image brilliance results when the area of the aperture is doubled or halved. Multiplying the diameter of any circle by 1.4 yields a larger circle with 2x greater surface area. Conversely, dividing the diameter of any circle by 1.4 calculates a reduced diameter circle with half the surface area. This is the basis of the f-number system with its 2x incremental delta.

The inverse of 1.4 is 1/1.4 = 0.71. Now instead of dividing by 1.4, we substitute multiplication by 0.71. This value is chosen as a focal reducer factor because it shortens the focal length exactly the required amount to achieve a 2x increase in image brightness (1 f-stop). This fact is governed by the law of the inverse square. This law lays down the principles of how light intensity changes with distance.

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