Calculate the position of a 3 cm high object, if it is to produce a 6 cm size real image, using a focal length convex lens of 8 cm.
To calculate the position of the object for a convex lens, we can use the lens formula:
1/f = 1/v - 1/u
where:
- f is the focal length of the convex lens
- v is the image distance (distance between the lens and the image)
- u is the object distance (distance between the lens and the object)
Given:
- Height of the object (h) = 3 cm
- Size of the real image (h') = 6 cm
- Focal length (f) = 8 cm
Step 1: Convert all measurements to meters
- Height of the object (h) = 3 cm = 0.03 m
- Size of the real image (h') = 6 cm = 0.06 m
- Focal length (f) = 8 cm = 0.08 m
Step 2: Determine the object distance (u)
To find the object distance (u), we need to use the magnification formula:
m = h'/h = -v/u
where:
- m is the magnification
- h' is the size of the real image
- h is the height of the object
Given that the magnification (m) is h'/h = 0.06/0.03 = 2
From the lens formula, we can rearrange and solve for u:
1/f = 1/v - 1/u
Simplifying, we get:
1/u = 1/v - 1/f
Plugging in the given values:
1/u = 1/v - 1/f
1/u = 1/0.06 - 1/0.08
1/u = (1/0.06 - 1/0.08) / 1
Simplifying further gives:
1/u = (-4/0.24) / 1
1/u = -16.67
u = -1/16.67
u = -0.06 m
Note: The negative sign indicates that the object distance is on the opposite side of the lens (in front of the lens).
Therefore, the position of the object is at -0.06 meters or -6 cm in front of the convex lens.