Question

You want to create a lens that will magnify an image by m=3.42, and produce an image that you see located 5cm behind the lens. Where would you put the object relative to the lens to produce this? (A positive value is behind the lens, a negative value is infront of the lens.)

Answer 1

The object should be placed 1.46 cm in front of the lens to achieve a magnification of 3.42 with the image appearing 5 cm behind the lens.

Step-by-step explanation:

To find the object distance (do) where an image will appear with a magnification of m=3.42 and seen located 5cm behind the lens, we use the lens magnification equation m = -di/do, where di is the image distance and do is the object distance. First, we must address that the positive value of the image distance indicates that the image is virtual and located on the same side of the lens as the object. Since m is positive, the image is upright with respect to the object.

To solve the problem, we rearrange the magnification equation to solve for do:

do = -di/m = -(5 cm)/3.42

Calculation gives us:

do = -1.46 cm

Thus, the object should be placed 1.46 cm in front of the lens to achieve the desired magnification.