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 eye and the image of the butterfly in the mirror? Explain your reasoning. We also have to make a sketch. I have no idea how to do this.
The image of the butterfly is 20 cm behind the mirror. Your eye is 50 cm in front of the mirror. The total distance between them is 70 cm.
You------B--|--B
<-----50--->|20>
To solve this problem, we need to understand the concept of image formation in a plane mirror.
1. Start by making a sketch:
Butterfly (B) --> Mirror --> You (Y)
2. According to the given information, the butterfly is 20 cm in front of the mirror. So, mark the butterfly (B) 20 cm in front of the mirror.
3. Now, you are positioned 50 cm behind the mirror. Mark your position with (Y) 50 cm behind the mirror.
4. Draw a dotted line from the butterfly (B) to the mirror. This line represents the incident ray.
5. According to the laws of reflection, when a ray of light strikes a plane mirror, it reflects back at an equal angle. Therefore, draw another dotted line extending behind the mirror, making the same angle with the mirror as the incident ray.
6. The point where the extended reflected ray intersects the line of sight (from you to the mirror) gives the location of the image of the butterfly (B').
7. Measure the distance from your position (Y) to the point where the extended reflected ray intersects the line of sight, which represents the distance between your eye and the image of the butterfly in the mirror.
8. The measured distance will be the answer to the problem.
Remember, in this case, since you are behind the mirror, the image will appear virtual and will be formed on the same side as the object.
Note: The sketch is essential to visualize the problem and ensure accurate measurements.
To solve this problem, let's start by understanding how a plane mirror works. A plane mirror creates a virtual reflection of an object without changing its size or orientation. The image appears to be located behind the mirror, at the same distance as the object from the mirror.
Now, let's create a sketch to visualize the given scenario. Start by drawing a vertical line to represent the plane mirror. Label it as "Mirror." Draw a butterfly in front of the mirror, labeled as "Butterfly." Indicate that the butterfly is 20 cm away from the mirror by drawing a horizontal line between the butterfly and mirror, labeled as "20 cm." Furthermore, draw yourself behind the mirror, 50 cm away from it, labeled as "You."
Now, we need to find the distance between your eye and the image of the butterfly in the mirror. To do this, we can use the concept of virtual images and the fact that the image appears to be at the same distance as the object.
From your position, imagine drawing a straight line that extends from your eye, passes through the mirror, and reaches the image of the butterfly. Since the butterfly is 20 cm away from the mirror, the image will also be 20 cm away from the mirror, but on the opposite side. So, we can draw a dotted line extending from the butterfly's position on the other side of the mirror, labeled as "Virtual Image."
Finally, measure the distance between your eye position and the virtual image of the butterfly. In this case, the distance between your eye and the virtual image of the butterfly is 50 cm + 20 cm = 70 cm.
Therefore, the distance between your eye and the image of the butterfly in the mirror is 70 cm.
Remember, when dealing with plane mirrors, the distance between the object and the mirror is the same as the distance between the image and the mirror. This concept can be applied to solve various problems involving plane mirrors.