Final Answer:
The formula for the angular magnification (M) of a convex lens with focal length (f) when the eye is very close to the lens and the near point is at a distance (D) from the eye is given by M = -f / (f - D).
Step-by-step explanation:
The angular magnification of a lens describes how much larger an object appears when viewed through the lens. When the eye is very close to the lens, the final image is formed at the least distance of distinct vision (D). In this scenario, the formula for angular magnification (M) for a convex lens is M = -f / (f - D), where f is the focal length of the lens.
The negative sign in the formula indicates that the image is virtual and upright, which is common when the object is brought within the least distance of distinct vision. The formula shows that as the distance (D) approaches the focal length (f), the angular magnification increases significantly. Conversely, as the object is moved away from the lens, resulting in an increase in the distance (D), the magnification decreases.
The calculation involves substituting the given values of the focal length (f) and the distance (D) into the formula M = -f / (f - D). This equation provides the angular magnification (M) of the convex lens when the eye is very close to the lens and the near point is at a distance (D) from the eye. Understanding this formula helps determine how much larger an object will appear when viewed through such a lens configuration, crucial in various optical applications and understanding human vision.