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

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2.2

To determine the position of the final image formed by the magnification of the two lenses, we need to use the lens formula and the lens maker's formula.

1) Position of the Final Image:
First, we need to find the image formed by lens A. Using the lens 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:
F1 = focal length of lens A = 20 cm
Object distance for lens A, u1 = F0 = 0 cm

Substituting the values into the lens formula, we get:

1/20 = 1/v1 - 1/0

Since the object distance is 0, the second term on the right side becomes infinite. Therefore, 1/v1 is also infinite, implying that the image formed by lens A will be at infinity.

Now, we need to find the distance between the first image and the second lens, which is equal to the object distance for lens B.

The object distance for lens B, u2 = distance between the lenses - distance between the first lens and the first image.
Given:
Distance between the lenses = 80 cm
Distance between the first lens and the first image (formed by lens A) = infinity

Therefore, u2 = 80 - ∞ (infinity)

As we subtract infinity from any finite distance, the result will still be infinity.

Now, we can find the image formed by lens B using the lens formula:

1/F2 = 1/v2 - 1/u2

Substituting the values, we get:

1/25 = 1/v2 - 1/∞

Since the object distance is infinite, the second term on the right side becomes zero. Therefore, 1/v2 is equal to 1/25.

Simplifying, we find that v2 = 25 cm.

So, the position of the final image formed by the magnification of the two lenses is 25 cm from the second lens.

2) Magnification of the Final Image:
To find the magnification of the final image, we can use the magnification formula:

Magnification (m) = v/u

where v is the image distance and u is the object distance.

Using the values obtained earlier:
v2 = 25 cm (image distance for the final image)
u2 = ∞ (object distance for the final image)

Since the object distance is infinite, the magnification of the final image will also be zero.

Therefore, the magnification of the final image formed by the combination of the two lenses is zero.

To determine the position of the final image formed by the magnification of the two lenses, we need to use the lens formula and the magnification formula.

1) Position of the final image:
- Lens A has a focal length F1 = 20cm, and the object is placed F0 = 20cm in front of it.
- Using the lens formula: 1/F1 = 1/v1 - 1/u1, where v1 is the image distance and u1 is the object distance from lens A.
- Rearranging the formula: 1/v1 = 1/F1 + 1/u1
1/v1 = 1/20 + 1/20 (since u1=F0=20)
1/v1 = 1/20 + 1/20
1/v1 = 2/20
1/v1 = 1/10
v1 = 10cm

- Now, lens B has a focal length F2 = 25cm, and the object distance for lens B is u2 = 10cm (since v1 = 10cm).
- Again, using the lens formula: 1/F2 = 1/v2 - 1/u2
- Rearranging the formula: 1/v2 = 1/F2 + 1/u2
1/v2 = 1/25 + 1/10 (since u2=v1=10)
1/v2 = 2/50 + 5/50 (finding a common denominator)
1/v2 = 7/50
v2 = 50/7 ≈ 7.14cm

Therefore, the final image formed by the magnification of the two lenses is located approximately 7.14cm from lens B.

2) Magnification of the final image:
- The magnification of each lens is given by the formula: M = -v/u, where M is the magnification, v is the image distance, and u is the object distance.
- For lens A, the magnification is M1 = -v1/u1 = -10/20 = -1/2.
- For lens B, the magnification is M2 = -v2/u2 = -(50/7)/(10) = -5/7.
- To find the overall magnification when two lenses are combined, we multiply the individual magnifications: M_total = M1 * M2 = (-1/2) * (-5/7) = 5/14.

Therefore, the magnification of the final image formed by the combination of the two lenses is 5/14.