To solve this problem, we can use the lens formula:
1/f = 1/v - 1/u
where:
- f is the focal length of the lens,
- v is the image distance, and
- u is the object distance.
Given that the focal length (f) is 15.5 cm and the magnification (M) is 3.1, we can also use the magnification formula:
M = -v/u
Since the image is virtual and upright, the magnification (M) should be positive.
Let's solve for the object distance (u) using the magnification formula:
M = -v/u
3.1 = -v/u (since M is positive)
-3.1u = v
Now, we substitute this value of v into the lens formula:
1/f = 1/v - 1/u
1/15.5 = 1/(-3.1u) - 1/u
To simplify this equation, let's find a common denominator:
1/15.5 = (-1 + 3.1) / (3.1u)
Multiplying both sides of the equation by 15.5 and simplifying:
1 = (2.1) / (3.1u)
Cross-multiplying:
3.1u = 2.1
Now, solve for u:
u = 2.1 / 3.1
u ≈ 0.6774 cm
Therefore, the object is approximately 0.6774 cm away from the lens.