The vehicle located 4 meters behind the bike will have a virtual image formed 2 meters behind the convex mirror.
To calculate the location and position of a vehicle which is 4 meters behind the bike as seen in the convex mirror, we can use the mirror equation and ray diagram.
1. Mirror equation:
The mirror equation is given by:
1/f = 1/v + 1/u
where f is the focal length of the mirror, v is the image distance, and u is the object distance.
2. Given information:
- Radius of curvature (R) = 2 meters (for a convex mirror, R is positive)
- Object distance (u) = -4 meters (negative because the object is behind the mirror)
3. Calculation of focal length:
The focal length of a convex mirror is half of the radius of curvature, so:
f = R/2 = 2/2 = 1 meter
4. Calculation of image distance:
Substituting the given values into the mirror equation, we can solve for the image distance (v):
1/1 = 1/v + 1/-4
1 = 1/v - 1/4
1 = (4-v)/4v
4v = 4(4-v)
4v = 16 - 4v
8v = 16
v = 16/8
v = 2 meters
Therefore, the image of the vehicle is formed at a distance of 2 meters behind the convex mirror.
Ray Diagram:
To explain the position of the image using a ray diagram:
- Draw an arrow representing the vehicle at a distance of 4 meters behind the convex mirror.
- Draw a ray from the top of the arrow parallel to the principal axis, which gets reflected off the mirror as if it is coming from the focal point (1 meter behind the mirror).
- Draw a ray from the top of the arrow towards the center of curvature of the mirror (2 meters in front of the mirror), which gets reflected back along the same path.
- The intersection point of these two rays represents the virtual image of the vehicle, which is formed 2 meters behind the convex mirror.