Final answer:
The distance from the objective to the object being viewed is calculated using the lensmaker's equation, considering the final image is at infinity. By working through the lens equation for the objective lens, the distance is found to be approximately 8.31 mm.
Step-by-step explanation:
The question relates to the operation of a microscope and requires the application of lens formulas to determine the distance from the objective lens to the object being viewed. To solve this, we use the lensmaker's equation 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the distance from the lens to the object, and di is the distance from the lens to the image.
For the objective lens in a compound microscope, the image formed is real and inverted. Since the final image formed by the eyepiece is at infinity, the intermediate image (formed by the objective lens) must be located at the focal point of the eyepiece. Therefore, the distance of this intermediate image from the objective lens is 18.0 mm (the focal length of the eyepiece) plus 19.7 cm (the distance between the eyepiece and the objective), which equals 197 mm + 18 mm = 215 mm. This is the image distance (di) for the objective lens.
Using the lens equation for the objective lens with a focal length of 8.00 mm:
- 1/f = 1/do + 1/di
- 1/8 mm = 1/do + 1/215 mm
- 1/do = 1/8 mm - 1/215 mm
- 1/do = (215 - 8)/(8 * 215) mm
- 1/do = 207/1720 mm
- do = 1720/207 mm
- do ≈ 8.31 mm
Therefore, the distance from the objective to the object is approximately 8.31 mm.