An object is placed 20cm in
front of a concave mirror whose
focal length is 10cm. where and
how is the image formed?
A. Center of curvature and
inverted
B. 20cm behind the mirror and
inverted
C. 20cm in front of the mirror and
upright
D. 20cm in front of the mirror and
virtual
The correct answer is D. 20cm in front of the mirror and virtual.
When an object is placed in front of a concave mirror, if the object is located between the focal point (F) and the mirror, the image formed is virtual (i.e., not real) and located behind the mirror. In this case, the object is placed 20cm in front of the mirror, which is between the focal point and the mirror surface. Therefore, the image will be formed 20cm in front of the mirror and it will be virtual.
To determine where and how the image is formed, we can use the mirror equation:
1/f = 1/dₒ + 1/dᵢ
Where:
- f = focal length of the mirror
- dₒ = object distance (distance from the object to the mirror)
- dᵢ = image distance (distance from the mirror to the image)
In this case, the object distance (dₒ) is given as 20 cm and the focal length (f) is given as 10 cm.
Plugging these values into the equation:
1/10 = 1/20 + 1/dᵢ
Simplifying the equation, we find:
1/dᵢ = 1/10 - 1/20 = 2/20 - 1/20 = 1/20
Therefore, the image distance is 20 cm.
Now, we can determine the characteristics of the image:
If the image distance (dᵢ) is positive, the image is formed on the same side as the object - in front of the mirror. Since the image distance is 20 cm, the image is formed 20 cm in front of the mirror.
If the image distance (dᵢ) is negative, the image would be formed on the opposite side of the object - behind the mirror. But since the image distance is positive in this case, option B can be eliminated as a possible answer.
Regarding the orientation of the image, when the image distance is positive, the image formed by a concave mirror is always inverted. Therefore, the correct answer is:
C. 20cm in front of the mirror and upright