Final answer:
The focal length of the corrective lens needed for the physicist's myopic eye is -23 cm, and the power of the lens is approximately -4.35 diopters.
Step-by-step explanation:
To correct the myopia of the physicist whose left eye can see clearly only up to a distance of 23 cm, we need to determine the focal length and the power of the corrective lens. The far point of myopic eyes is closer than normal, and a diverging (concave) lens is required to extend the image formation to the retina.
Using the lens formula 1/f = 1/v - 1/u, where f is the focal length of the lens, v is the image distance (distance from the lens where the image is formed), and u is the object distance (distance from the lens to the far point of the eye), we have:
Therefore, 1/f = 1/∞ - (-1/23), simplifying to f = -23 cm. The negative sign indicates a diverging lens is needed. To find the power P, we use the formula P = 1/f (with f in meters). So P = -100/23 diopters, accounting for the lens being 2 cm in front of the eye. Therefore, the corrective lens needs to have a focal length of -23 cm and a power of approximately -4.35 diopters.