An object 5cm high is placed at a distance of 12cm from a convex lens of focal length 8cm calculate the position and magnification of the image
Given:
- Object height (h1) = 5 cm
- Object distance (d1) = 12 cm
- Focal length (f) = 8 cm
We can use the lens formula to calculate the image distance (d2) and magnification (m).
Lens formula:
1/f = 1/d1 + 1/d2
Substituting the given values:
1/8 = 1/12 + 1/d2
Simplifying the equation:
1/d2 = 1/8 - 1/12
1/d2 = (12 - 8)/(12 * 8)
1/d2 = 4/96
1/d2 = 1/24
d2 = 24 cm
Now, we can calculate the magnification:
Magnification formula:
m = -d2/d1
Substituting the values:
m = -24/12
m = -2
Therefore, the position of the image is 24 cm from the lens on the other side of the object, and the magnification is -2.
To calculate the position and magnification of the image formed by a convex lens, we can use the lens formula and magnification formula.
1. Lens formula:
The lens formula is given by:
1/f = 1/v - 1/u
Where:
f is the focal length of the lens
v is the image distance from the lens (positive for a real image, negative for a virtual image)
u is the object distance from the lens (positive if the object is on the same side as the incident light, negative if the object is on the opposite side)
2. Magnification formula:
The magnification formula is given by:
magnification (m) = height of image (h') / height of object (h)
Given:
Height of object (h) = 5 cm
Object distance from the lens (u) = 12 cm
Focal length of the lens (f) = 8 cm
Now, let's calculate the position and magnification of the image step by step:
Step 1: Calculate the image distance (v) using the lens formula:
1/f = 1/v - 1/u
Substituting the given values:
1/8 = 1/v - 1/12
Simplifying the equation:
1/v = 1/8 + 1/12
1/v = (3 + 2) / 24
1/v = 5/24
Taking the reciprocal of both sides:
v = 24/5
v ≈ 4.8 cm
So, the image distance from the lens (v) is approximately 4.8 cm.
Step 2: Calculate the magnification (m):
magnification (m) = h' / h
Given:
Height of object (h) = 5 cm
To calculate the height of the image (h'), we can use the similar triangles formed by the object and the image.
Using the magnification formula:
m = h' / h
m = h' / 5
Since the image is formed by a convex lens, the image is virtual and erect. Therefore, the height of the image (h') is equal to the height of the object (h).
So, substituting h' = h = 5 cm in the magnification formula:
m = 5 / 5
m = 1
Therefore, the magnification (m) is 1.
Step 3: Analyzing the position and magnification of the image:
- The image distance (v) is approximately 4.8 cm from the lens, on the same side as the object. The positive sign indicates that the image is real.
- The magnification (m) is 1, which means the height of the image is the same as the height of the object. The positive value indicates an upright image.
In summary, the image is real, located approximately 4.8 cm from the lens, and its height is the same as the height of the object.