A butterfly at eye level is 18 cm in front of an plane mirror. You are behind the butterfly, 45 cm from the mirror. What is the distance between your eye and the image of the butterfly in the mirror?
you are 45+18cm from the image.
To find the distance between your eye and the image of the butterfly in the mirror, we can use the concept of virtual images formed by a plane mirror.
Given:
Distance of butterfly from the mirror (object distance), d1 = 18 cm
Distance of your eye from the mirror (observer distance), d2 = 45 cm
In the case of a plane mirror, the image formed is virtual and appears to be as far behind the mirror as the object is in front of it. This means that the distance between the object and its image is equal to twice the distance between the object and the mirror.
So, the distance between the butterfly and its image in the mirror (image distance), d3, can be calculated as:
d3 = 2 * d1 = 2 * 18 cm = 36 cm
Now, to find the distance between your eye and the image of the butterfly in the mirror, we add the distance between your eye and the mirror (d2) to the distance between the butterfly and its image in the mirror (d3):
Distance between your eye and the image of the butterfly in the mirror = d2 + d3 = 45 cm + 36 cm = 81 cm
Therefore, the distance between your eye and the image of the butterfly in the mirror is 81 cm.
To find the distance between your eye and the image of the butterfly in the mirror, we can use the concept of virtual images formed by plane mirrors.
1. First, let's label the given distances:
- Distance from the butterfly to the mirror (object distance) = 18 cm
- Distance from your eye to the mirror = 45 cm
2. Since the butterfly is in front of the mirror, its image will be formed behind the mirror. We need to calculate the position of this virtual image.
3. By using the properties of plane mirrors, we know that the image distance (di) is equal to the object distance (do). Therefore, in this case, di = do = 18 cm.
4. Now, we can calculate the total distance between your eye and the image of the butterfly in the mirror. This can be done by adding the distances from your eye to the mirror (45 cm) and from the mirror to the virtual image (18 cm):
Total distance = Distance from your eye to the mirror + Distance from the mirror to the virtual image
= 45 cm + 18 cm
= 63 cm
Therefore, the distance between your eye and the image of the butterfly in the mirror is 63 cm.