Final answer:
The image will be formed at a distance of 7.5cm behind the concave mirror, and it will be real and inverted.
Step-by-step explanation:
To find the distance from the concave mirror where the image will be formed, you can use the mirror formula:
1/f = 1/do + 1/di
Where f is the focal length of the mirror, do is the distance of the object from the mirror, and di is the distance of the image from the mirror.
In this case, the focal length (f) of the concave mirror is -10cm (negative because it's a concave mirror), and the distance of the object (do) is 30cm. Plugging these values into the formula, we get:
1/-10 = 1/30 + 1/di
Simplifying the equation, we find:
1/di = 1/-10 - 1/30 = -1/15 - 1/30 = -3/30 - 1/30 = -4/30
So, 1/di = -4/30. Taking the reciprocal of both sides, we get:
di = -30/4 = -7.5cm
Since the distance from a mirror is always positive, the image will be formed at a distance of 7.5cm behind the mirror.
The characteristics of the image formed by the concave mirror can be determined by considering the object's position relative to the focal point of the mirror:
- If the object is placed farther than the focal length from the mirror, the image will be formed on the same side as the object, real, and inverted
- If the object is placed at the focal length from the mirror, the image will be formed at infinity and will be real and inverted.
- If the object is placed between the focal length and the mirror, the image will be formed on the opposite side of the object, virtual, and upright.
Since the object in this case is placed at a distance of 30cm in front of the concave mirror, which is greater than the focal length of 10cm, the image will be formed on the same side as the object, real, and inverted.