To determine which optical instrument can best be constructed with converging lenses of focal lengths 50 cm and 5 cm, let's analyze each option and understand the principles behind the functioning of these optical devices. ### Correct Option: D. Astronomical telescope #### Explanation of Why the Answer is Correct: 1. **Understanding the Astronomical Telescope**: - An astronomical telescope is designed to observe distant celestial objects. It typically consists of two converging lenses: the objective lens (which has a longer focal length) and the eyepiece lens (which has a shorter focal length). - The objective lens gathers light from a distant object and forms a real image, which is then magnified by the eyepiece lens for viewing. 2. **Focal Lengths**: - In this case, we have two lenses: one with a focal length of 50 cm (which we will use as the objective lens) and another with a focal length of 5 cm (which will serve as the eyepiece). - The longer focal length (50 cm) is suitable for the objective lens because it allows for the collection of light from distant stars and planets, forming a clear image. - The shorter focal length (5 cm) is appropriate for the eyepiece, as it provides a higher magnification of the image formed by the objective lens. 3. **Magnification Calculation**: - The total magnification (M) of an astronomical telescope can be calculated using the formula: \[ M = \frac{f_{\text{objective}}}{f_{\text{eyepiece}}} \] - Substituting the values: \[ M = \frac{50 \text{ cm}}{5 \text{ cm}} = 10 \] - This means the telescope will magnify the image by a factor of 10, which is suitable for observing celestial objects. ### Why the Other Options Are Incorrect: A. **Compound Microscope**: - A compound microscope uses two converging lenses, but the configuration is different. The objective lens has a shorter focal length than the eyepiece lens, which is the opposite of what we have here (50 cm and 5 cm). - Therefore, this option is not suitable because the focal lengths do not match the requirements for a compound microscope. B. **Galileo's Telescope**: - Galileo's telescope uses a concave eyepiece and a convex objective lens. The focal lengths required for this type of telescope do not match the given lenses, as it requires a longer focal length for the eyepiece compared to the objective. - Thus, this option is also incorrect. C. **Terrestrial Telescope**: - A terrestrial telescope is similar to an astronomical telescope but is designed for viewing objects on Earth. It typically uses a combination of lenses to correct the image orientation. - However, the configuration of the lenses (focal lengths) does not align with the requirements for a terrestrial telescope, which usually requires a different arrangement of focal lengths. ### Summary of Key Points: - The correct answer is **D. Astronomical telescope** because it uses a longer focal length for the objective lens (50 cm) and a shorter focal length for the eyepiece (5 cm). - The magnification of the telescope is calculated to be 10, making it suitable for observing distant celestial objects. - Other options are incorrect due to mismatched configurations of focal lengths and lens types required for those specific instruments. ### Revision Summary: - An astronomical telescope uses a long focal length for the objective and a short focal length for the eyepiece. - The magnification formula is \( M = \frac{f_{\text{objective}}}{f_{\text{eyepiece}}} \). - A compound microscope requires the opposite configuration of focal lengths. - Galileo's and terrestrial telescopes have specific requirements that do not match the given lenses.