a butterfly at eye level is 20 cm in front of a plane mirror. you are behind the butterfly, 50 cm from the mirror. what is the distance between your eyes and the image of the buterfly in the mirror?

plane mirror puts the image at -20cm, so the distance is 70cm.

To solve this problem, we can use the concept of reflection in a plane mirror. The key here is to understand that the image formed by a plane mirror is at the same distance behind the mirror as the object is in front of the mirror.

Given:
Distance between the butterfly and the mirror (object distance) = 20 cm
Distance between you and the mirror = 50 cm

To find the distance between your eyes and the image of the butterfly, we need to consider two distances: the distance between your eyes and the mirror (eye-mirror distance), and the distance between the mirror and the image (mirror-image distance).

1. The mirror-image distance:
Since a plane mirror produces a virtual image, the mirror-image distance will be equal to the object distance. In this case, the mirror-image distance is also 20 cm.

2. The eye-mirror distance:
This is the distance between your eyes and the plane mirror. Given that the distance between you and the mirror is 50 cm, the eye-mirror distance will be 50 cm.

3. Distance between your eyes and the image:
To find this, we need to calculate the difference between the eye-mirror distance and the mirror-image distance.

Distance between your eyes and the image = eye-mirror distance - mirror-image distance
Distance between your eyes and the image = 50 cm - 20 cm
Distance between your eyes and the image = 30 cm

Therefore, the distance between your eyes and the image of the butterfly in the mirror is 30 cm.