Answer:When a 4.5 cm needle is placed 12 cm away from a convex mirror with a focal length of 15 cm, the image formed will be virtual, upright, and reduced in size.
To determine the location of the image, we can use the mirror formula:
1/f = 1/v - 1/u
where f is the focal length, v is the image distance from the mirror, and u is the object distance from the mirror.
In this case, the focal length (f) is 15 cm, and the object distance (u) is 12 cm. Plugging these values into the formula, we get:
1/15 = 1/v - 1/12
Solving this equation, we find that the image distance (v) is approximately 60 cm.
The magnification (m) can be calculated using the formula:
m = -v/u
Plugging in the values, we get:
m = -60/12 = -5
So, the magnification is -5, indicating that the image is reduced in size.
As the needle is moved farther from the mirror, the image will move closer to the mirror and become larger. This is because the object distance (u) will increase, leading to a decrease in the image distance (v) and an increase in magnification (m).
In summary, when a 4.5 cm needle is placed 12 cm away from a convex mirror with a focal length of 15 cm, the image formed is virtual, upright, and reduced in size. The location of the image is approximately 60 cm from the mirror, and the magnification is -5. As the needle is moved farther from the mirror, the image moves closer to the mirror and becomes larger.
Step-by-step explanation: