The objective lens of a microscope has a focal length of 2cm and that of the eyepiece is 2.2cm and they are placed 8cm and 3cm apart from the objective lens.Find the distance of the;

a)image I from the objective lens
b)final image

first, I would draw a ray diagram (to be used later).

Then, do the formulas you already know for each lens, and on the second lens, you will have to calculate the fo from the first image.

To find the distance of the image (I) from the objective lens, 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 (positive when on the opposite side of the incident light),
- u is the object distance from the lens (positive when on the same side as the incident light).

Given:
- The focal length of the objective lens (f₁) = 2 cm.
- The object distance from the objective lens (u₁) = 8 cm.

Let's solve for v₁ (the distance of the image from the objective lens):

1/2 = 1/v₁ - 1/8

Rearranging the equation:

1/v₁ = 1/2 + 1/8

1/v₁ = 4/8 + 1/8

1/v₁ = 5/8

v₁ = 8/5 cm

So, the distance of the image (I) from the objective lens is 8/5 cm.

To find the final image distance, we need to find the position of the eyepiece.

Given:
- The focal length of the eyepiece (f₂) = 2.2 cm.
- The object distance from the eyepiece (u₂) = 3 cm.

We can again use the lens formula, but this time with the eyepiece:

1/f = 1/v - 1/u

Plugging in the values:

1/2.2 = 1/v₂ - 1/3

Rearranging the equation:

1/v₂ = 1/2.2 + 1/3

1/v₂ ≈ 0.4545 + 0.3333

1/v₂ ≈ 0.7878

v₂ ≈ 1.27 cm

Since the eyepiece is closer to the observer, the final image will be formed at a distance of v₂ from the eyepiece. Therefore, the distance of the final image is approximately 1.27 cm from the eyepiece.