Question

A magnifying glass has a convex lens with focal length of 6.60 and I being used to study a picture. What height would the magnifying glass need to be held above the picture in order for it to appear twice as large?

Answer 1

The magnifying glass needs to be held approximately 3.30_ above the picture to make it appear twice as large.

Step-by-step explanation:

To determine the height at which the magnifying glass needs to be held, we can use the magnification formula for a convex lens:
`\(m = 1 + (d)/(f)\), where \(m\)` is the magnification,
`\(d\)` is the distance between the lens and the object, and
`\(f\)` is the focal length of the lens. Since the magnifying glass is used to view the picture, and the requirement is for the picture to appear twice as large
`(\(m = 2\)`), we rearrange the formula to solve for
`\(d\): \(d = (m - 1) * f\)`. Plugging in the given focal length
`(\(f = 6.60\))` and the desired magnification
`(\(m = 2\)), we get \(d = (2 - 1) \` times
`6.60 = 6.60\)`. This result represents the distance between the picture and the magnifying glass.

However, this distance refers to the combined distance from the lens to the picture and from the lens to the eye. Since the magnification formula uses the total distance between the lens and the object, and the distance between the picture and the lens is half of the total distance, we divide the calculated distance by 2 to find the height at which the magnifying glass needs to be held:
`\(h = (6.60)/(2) = 3.30\)`. Thus, the magnifying glass should be held approximately 3.30_ above the picture to achieve a magnification where the picture appears twice as large when viewed through the lens.