Physics
Physics
Problem
(i) Draw a neat, labelled ray diagram to show the formation of a virtual image by a single converging lens when it is used as a reading magnifier with the final image situated at the least distance of distinct vision, D. (ii) Starting from suitable expressions for the angular sizes of the object with and without the lens, derive an expression for the angular magnification of the magnifier in terms of D and the focal length f of the lens. (iii) Keeping D fixed, explain qualitatively how the magnifying power varies with the focal length of the lens. (iv) Give one reason why a lens of extremely small focal length is not generally preferred for ordinary reading even though it offers higher magnification.Intuitive explanation
When you use a magnifying glass for reading, the lens bends light so that a virtual image forms at your eye's comfortable viewing distance—the least distance of distinct vision, . Angular magnification compares how much larger the image appears to your eye (measured by the angle it subtends) versus viewing the object with the naked eye at distance . The key insight is that magnification depends on the ratio of these two angles: one determined by the lens's focusing power and one by simple geometry at distance . Understanding how focal length controls this angle ratio reveals why shorter focal lengths give higher magnification, but practical limits exist.
Intuitive explanation
When you use a magnifying glass for reading, the lens bends light so that a virtual image forms at your eye's comfortable viewing distance—the least distance of distinct vision, . Angular magnification compares how much larger the image appears to your eye (measured by the angle it subtends) versus viewing the object with the naked eye at distance . The key insight is that magnification depends on the ratio of these two angles: one determined by the lens's focusing power and one by simple geometry at distance . Understanding how focal length controls this angle ratio reveals why shorter focal lengths give higher magnification, but practical limits exist.