an object of size 3 cm is place 10 cm away from the convex lens find the position nature and size of the images it focal length is 7 cm.
To determine the position, nature, and size of the image formed by a convex lens, we can use the lens formula and magnification formula.
1. Lens formula:
The lens formula relates the object distance (u), the image distance (v), and the focal length of the lens (f) as follows:
1/f = 1/v - 1/u
2. Magnification formula:
The magnification formula relates the height of the image (h') to the height of the object (h):
Magnification (m) = h'/h = -v/u
Given values:
Object size (h) = 3 cm
Object distance (u) = -10 cm (negative sign indicates it is placed on the same side as the object)
Focal length (f) = 7 cm
Now, let's calculate the position, nature, and size of the image:
1. Position of the image (v):
Using the lens formula:
1/f = 1/v - 1/u
Substituting the given values:
1/7 = 1/v - 1/-10
Solving for v:
1/v = 1/7 + 1/10
1/v = (10 + 7) / (7 * 10)
1/v = 17 / 70
v = 70 / 17
Therefore, the position of the image (v) is approximately 4.12 cm.
2. Nature of the image:
Since the object is placed outside the focal length (u < f), the image will be real, inverted, and on the opposite side as the object.
3. Size of the image (h'):
Using the magnification formula:
Magnification (m) = h'/h = -v/u
Substituting the given values:
m = h'/3 = -(4.12) / (-10)
Solving for h':
h' = 3 * (-4.12) / (-10)
h' = 12.36 / 10
h' = 1.236 cm
Therefore, the size of the image (h') is approximately 1.236 cm.
In conclusion, the position of the image is approximately 4.12 cm, the nature of the image is real and inverted, and the size of the image is approximately 1.236 cm.