Final answer:
To find the object distance (do) when magnification (m) is -0.40 and focal length (f) is 60 cm, we rearrange the magnification formula to do = f/(1 + 1/m), resulting in an object distance of 40 cm in front of the lens.
Step-by-step explanation:
Finding the Object Distance (do)
To find David's perception of Rebecca's distance, represented as the object distance (do), we use the lens formula and magnification. Given that the magnification (m) is -0.40 and the focal length (f) is 60 cm, we first need to recall the lens formula and magnification relationship:
- Lens Formula: 1/f = 1/do + 1/di
- Magnification: m = -di/do
From the magnification formula, we can solve for do. With m = -0.40, we rearrange the formula to find do = -di/m. To find di, we need to use the lens formula. However, the problem does not directly provide di, so we can use the relationship that derives from the lens formula:
m = f/(f - do), then substitute m = -di/do into the equation and solve for do.
After rearranging we get: do = f/(1 + 1/m). Plugging in the known values gives us:
do = 60 cm / (1 + 1/(-0.40)) = 60 cm / (1 - 2.5) = 60 cm / (-1.5) = -40 cm.
Since do is negative, it signifies the object is on the same side as the image (virtual image). However, in practice, distances in front of the lens are positive, so we can say the object is 40 cm away from the lens.