Question:
A concave mirror with a focal length of 20 cm is used to form an image of an object. The object is placed 30 cm in front of the mirror. Determine the characteristics of the image formed by the mirror using the mirror equation. Is the image real or virtual, upright or inverted? Also, calculate the magnification of the image.
Answer:
Given information:
Focal length (f) = -20 cm (negative sign indicates that it is a concave mirror)
Object distance (p) = -30 cm (negative sign indicates that the object is placed in front of the mirror)
To determine the characteristics of the image formed by the mirror, we can use the mirror equation:
1/f = 1/p + 1/q
Where: f = focal length p = object distance q = image distance
Rearranging the equation to solve for image distance (q):
1/q = 1/f - 1/p
Substituting the given values:
1/q = 1/(-20 cm) - 1/(-30 cm)
Simplifying:
1/q = -3/(-20) - 2/(-20) 1/q = (3 + 2)/(-20) 1/q = 5/(-20)
Taking the reciprocal of both sides:
q = -20/5 q = -4 cm
The negative sign indicates that the image is formed on the same side as the object, which means it is a real image.
To determine whether the image is upright or inverted, we can analyze the sign convention. According to the sign convention for mirrors:
In this case, both p and q are negative, indicating that the object and image are formed on the same side of the mirror. Therefore, the image is inverted.
Lastly, let's calculate the magnification (m) of the image using the formula:
m = -q/p
Substituting the values:
m = -(-4 cm)/(-30 cm) m = 4/30 m = 0.1333
The negative sign indicates that the image is inverted, and the magnification value of 0.1333 indicates that the image is smaller than the object.
In conclusion, the characteristics of the image formed by the concave mirror are: