Final answer:
Using the lens formula, the object is found to be 14 cm away from a diverging lens with a focal length of 35 cm when the virtual image is located 10 cm from the lens.
Step-by-step explanation:
To determine how far an object is from a diverging lens when the virtual image is located 10 cm from the lens, we can use the lens formula: 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. For a diverging lens, the focal length is negative, so we have f = -35 cm. We also know that the image is virtual and on the same side of the lens as the object, making di negative; di = -10 cm.
Plugging the values into the lens formula, we get: 1/(-35 cm) = 1/do + 1/(-10 cm). This simplifies to: -1/35 = 1/do - 1/10. Solving for do, we find: 1/do = -1/35 + 1/10 = -1/35 + 3.5/35 = 2.5/35. Taking the reciprocal of both sides gives us do = 35/2.5 = 14 cm. Therefore, the object is located 14 cm from the lens.