An object is placed 15cm in front of a concave mirror of focal length 10cm.Find:
1.the position
2.nature
3.magnification of the image formed
1. To find the position of the image formed by the concave mirror, we can use the mirror formula:
1/f = 1/v - 1/u
where f is the focal length, v is the image distance, and u is the object distance.
Given:
f = -10 cm (since it is a concave mirror)
u = -15 cm (since the object is placed in front of the mirror)
Using the given values in the mirror formula:
1/-10 = 1/v - 1/-15
Simplifying:
-3/30 = 1/v + 1/15
Multiply through by 30v:
-3v = 30 + 2v
Combine like terms:
v = -30 cm
Therefore, the position of the image formed by the concave mirror is 30 cm behind the mirror.
2. To determine the nature of the image formed, we can use the magnification formula:
magnification (m) = -v/u
Given:
v = -30 cm
u = -15 cm
Using the given values in the magnification formula:
m = -(-30)/(-15) = 2
Since the magnitude of the magnification is greater than 1, the image formed is magnified. Therefore, the nature of the image is enlarged.
3. To find the magnification of the image formed by the concave mirror, we can use the magnification formula:
magnification (m) = -v/u
Given:
v = -30 cm
u = -15 cm
Using the given values in the magnification formula:
m = -(-30)/(-15) = 2
Therefore, the magnification of the image formed by the concave mirror is 2, indicating that the image is magnified by a factor of 2.