Final answer:
To calculate binocular decentration for spectacle lenses, use the lensmaker's equation considering the near point and image distances. Specifically, the power (P) is determined with P = 1/di + 1/do, where di is the image distance and do is the object distance from the lens.
Step-by-step explanation:
The formula to calculate binocular decentration, which refers to the necessary adjustments to align optical devices like binoculars or glasses with the eyes, generally involves using the lensmaker's equation and considering the distances from the spectacle lens to the near point and image distance. For spectacles, when an object is held at a distance of 25.0 cm (near vision) from the person's eyes, the spectacle lens must produce an image effectively at a distance of 1.00 m (the near point) for clear vision. The image distance (di) must be negative if it is on the same side of the spectacle as the object. Power (P) of a lens is given by P = 1/di + 1/do, where di is the image distance to the lens, and do is the object distance from the lens.
To calculate this for glasses worn for close vision, if the near point is 1.00 m away from the eye and the spectacle lens is 1.50 cm from the eye, we use the distances in the power equation. The object distance (do) would typically be the distance from the spectacle lens to the near point (25.0 cm) minus the thickness of the lens if significant. In this case, the image will be formed at a distance of 98.5 cm from the spectacle lens towards the object (di = -98.5 cm), considering the 1.5 cm lens-eye distance. The power of the spectacle lens can be calculated accordingly.