Two converging lenses, A and B,with focal length F1=20cm and F2=25cm,are placed 80cm apart. An object is placed F0cm in front of the first lens. 1)Determine the position of the final image formed by the magnification of the two lenses.
2)Determine the magnification of the final image formed by the combination of the two lenses
To determine the position of the final image formed by the magnification of the two lenses, we can use the lens formula:
1/f = 1/v - 1/u
where f is the focal length of the lens, v is the image distance from the lens, and u is the object distance from the lens.
Let's consider the first lens, lens A:
Given: F1 = 20 cm (focal length of lens A), F0 = -20 cm (object distance from lens A)
Plugging these values into the lens formula, we can find the image distance v1:
1/20 = 1/v1 - 1/-20
Simplifying this equation, we get:
1/20 = 1/v1 + 1/20
Multiply both sides by 20 × v1 to eliminate the denominators:
20 × v1 = 20 + v1
19 × v1 = 20
v1 = 20/19 cm
Now, we move on to the second lens, lens B:
Given: F2 = 25 cm (focal length of lens B), u2 = 80 cm (object distance from lens B)
Using the lens formula again, we can find the image distance v2:
1/25 = 1/v2 - 1/80
Simplifying this equation, we get:
1/25 = 1/v2 + 1/80
Multiply both sides by 25 × v2 to eliminate the denominators:
25 × v2 = 25 + v2
24 × v2 = 25
v2 = 25/24 cm
Now, to find the position of the final image, we consider the distance between lens A and lens B:
Given: Distance between lens A and lens B = 80 cm
Let's call the distance between lens A and the final image as d1, and the distance between lens B and the final image as d2.
d1 + d2 = 80
Since we know the image distance from both lenses (v1 and v2), we can find the individual distances:
d1 = 80 - v1 = 80 - 20/19 = 80 - 1.05 cm = 78.95 cm
d2 = 80 - v2 = 80 - 25/24 = 80 - 1.04 cm = 78.96 cm
Therefore, the position of the final image formed by the magnification of the two lenses is approximately 78.95 cm in front of lens A or 78.96 cm in front of lens B.
To determine the magnification of the final image formed by the combination of the two lenses, we use the magnification formula:
m = h'/h = -v2/v1
where h' is the height of the final image and h is the height of the object.
Since the magnification depends on the ratio of image distances from lens A and lens B, we can substitute the values and calculate:
m = -v2/v1 = -((25/24) / (20/19)) = -1.27
Therefore, the magnification of the final image formed by the combination of the two lenses is approximately -1.27.