To determine the location of the final image formed by the concave mirror and the plane mirror, we need to break down the problem step by step. Let's start by analyzing the concave mirror first, as it plays a crucial role in forming the initial image.
Step 1: Finding the Image from the Concave Mirror
The formula for the mirror equation is given by:
1/f = 1/v + 1/u
Where:
- f is the focal length of the mirror (for a concave mirror, it's negative).
- v is the image distance from the mirror.
- u is the object distance from the mirror (also negative for real objects).
In this case:
- Focal length, f = -21 cm (since it's a concave mirror).
- Object distance, u = -42 cm (the object is in front of the mirror).
Now, substituting these values into the mirror equation:
1/(-21) = 1/v + 1/(-42)
Rearranging gives:
1/v = 1/(-21) + 1/42
Finding a common denominator (which is 42):
1/v = -2/42 + 1/42 = -1/42
Thus, we find:
v = -42 cm
This negative value indicates that the image is formed 42 cm in front of the concave mirror, which means it is a real image located on the same side as the object.
Step 2: Position of the Image Relative to the Plane Mirror
The image formed by the concave mirror acts as a virtual object for the plane mirror. The distance from the concave mirror to the plane mirror is 21 cm. Since the image is 42 cm in front of the concave mirror, we can find the distance of this image from the plane mirror:
Distance from the image to the plane mirror = 42 cm - 21 cm = 21 cm
Now, this image is 21 cm in front of the plane mirror, which means it will reflect back to form another image.
Step 3: Finding the Final Image from the Plane Mirror
In a plane mirror, the image distance is equal to the object distance, but on the opposite side. Therefore, the final image will also be 21 cm behind the plane mirror.
Final Position of the Image
Since the plane mirror is located 21 cm in front of the concave mirror, the final image will be:
Distance from the concave mirror = 21 cm (to the plane mirror) + 21 cm (behind the plane mirror) = 42 cm
Thus, the final image is located 42 cm behind the concave mirror, which is the same distance as the original object but on the opposite side.
In summary, the final image formed by the combination of the concave mirror and the plane mirror is located 42 cm behind the concave mirror. This demonstrates how mirrors can interact to produce images at various locations based on their configurations and distances.
