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?
To find the distance between your eye and the image of the butterfly in the mirror, we can use the concept of virtual image formation in plane mirrors.
First, let's understand the scenario. The butterfly is 18 cm in front of the mirror, and you are behind the butterfly, 45 cm from the mirror. When you look at the mirror, you see the image of the butterfly formed behind the mirror.
Now, let's break down the steps to find the distance between your eye and the image of the butterfly in the mirror:
Step 1: Find the distance between the butterfly and the mirror.
The butterfly is 18 cm in front of the mirror.
Step 2: Find the location of the virtual image formed.
Since the mirror is a plane mirror, the virtual image formed is at the same distance behind the mirror as the object is in front of it. Therefore, the virtual image of the butterfly is also 18 cm behind the mirror.
Step 3: Find the distance between your eye and the mirror.
You are 45 cm behind the mirror.
Step 4: Calculate the distance between your eye and the image of the butterfly.
To get this distance, we need to consider the path of light rays from the virtual image to your eye. The light rays reflect off the mirror and reach your eye. Since the virtual image is formed 18 cm behind the mirror, the light rays travel an additional 18 cm from the image to the mirror and then 45 cm from the mirror to your eye. Therefore, the total distance between your eye and the image of the butterfly in the mirror would be 18 cm + 45 cm, which is equal to 63 cm.
So, the distance between your eye and the image of the butterfly in the mirror is 63 cm.
To find the distance between your eye and the image of the butterfly in the mirror, we can use the concept of virtual image and mirror formula.
Given:
Distance between the butterfly and the mirror (object distance), u = 18 cm
Distance between you and the mirror (eye distance), v = 45 cm
Using the mirror formula:
1/f = 1/u + 1/v
As the mirror is a plane mirror, the focal length (f) is infinity.
Substituting the given values into the formula, we have:
1/∞ = 1/18 + 1/45
Since 1/∞ = 0, we can simplify the equation by cross-multiplication:
1/18 + 1/45 = 1/v
Adding the fractions:
45/810 + 18/810 = 1/v
63/810 = 1/v
Now, cross-multiplying again:
63v = 810
Dividing both sides by 63:
v = 810 / 63
v ≈ 12.86 cm
Therefore, the distance between your eye and the image of the butterfly in the mirror is approximately 12.86 cm.