A butterfly at eye level is 21 cm in front of an plane mirror. You are behind the butterfly, 53 cm from the mirror. What is the distance between your eye and the image of the butterfly in the mirror?
What is 51+21?
To find the distance between your eye and the image of the butterfly in the mirror, we can use the mirror equation:
1/f = 1/d₀ + 1/dᵢ,
where:
- f is the focal length of the mirror,
- d₀ is the object distance (distance between the butterfly and the mirror),
- dᵢ is the image distance (distance between the mirror and the image).
Since the problem states that the butterfly is at eye level, we can assume its height is negligible compared to the distance between the butterfly and the mirror. Therefore, the mirror can be approximated as a plane mirror, which has a focal length of infinity.
Substituting the values into the equation, we get:
1/∞ = 1/53 + 1/dᵢ,
Simplifying the equation, we can remove the 1/∞ term:
0 = 1/53 + 1/dᵢ,
Next, we need to solve for dᵢ. Multiply both sides of the equation by (53 * dᵢ) to eliminate the denominators:
0 = (53 * dᵢ) / 53 + (53 * dᵢ) / dᵢ,
0 = dᵢ + 53.
Rearranging the equation, we get:
dᵢ = -53.
The negative sign indicates that the image is virtual, meaning it appears behind the mirror. However, since our eye is also behind the mirror, the distance between your eye and the virtual image, in this case, would be 53 cm.