Mirrors for astronomical instruments are invariably first-surface mirrors: The reflective coating is applied on the surface exposed to the incoming light. Household mirrors, on the other hand, are second-surface mirrors: The coating is applied to the back of the glass or plastic material of the mirror. (You can tell the difference by bringing the tip of an object close to the surface of the mirror. Object and image will nearly touch with a first-surface mirror; a gap will remain between them with a second-surface mirror.) Explain the reasons for these design differences.

First-surface mirrors are also called front surface mirrors. In these mirrors, the reflective coating is applied directly on the surface facing the incoming light. This means that the light directly reflects off the mirror's surface without passing through any other material.

Second-surface mirrors, or back surface mirrors, have the reflective coating applied to the rear side of the glass or plastic material. This means that the light will first pass through the glass or plastic material, then reflect off the coating, and finally pass through the material again before exiting the mirror.

In astronomical instruments, the use of first-surface mirrors is essential for the following reasons: 1. Minimal light loss: Since the light doesn't have to pass through any material before reflecting, there is minimal light loss in the process. This is crucial for observing dim objects in the night sky. 2. No ghost reflection: A second-surface mirror could cause a ghost reflection, where a portion of the light reflects off the front side of the glass. This phenomenon is eliminated in first-surface mirrors since the reflective surface is directly exposed to the incoming light. 3. Optimal image quality: First-surface mirrors provide better image quality since they aren't affected by the distortions or impurities in the glass or plastic material. This is critical for obtaining precise measurements and images in astronomical observations.

Second-surface mirrors are preferred for household use due to the following reasons: 1. Durability: The reflective coating is protected by the glass or plastic material, making the mirror more resistant to damage and wear, as opposed to a first-surface mirror where the coating is exposed and more susceptible to scratches or corrosion. 2. Cost-effectiveness: Second-surface mirrors are generally more affordable to produce because the manufacturing process is simpler, and the required tolerances for the glass or plastic material are not as strict as those for a first-surface mirror. 3. Aesthetic appeal: For most common household applications, the slight loss in image quality due to the additional reflections and material distortions isn't a significant concern. The appearance of the mirror, with its familiar reflective surface behind a layer of glass or plastic, provides a familiar and appealing look for household use. By understanding the differences and advantages of first-surface and second-surface mirrors, it becomes clear why first-surface mirrors are preferred in astronomical instruments, while second-surface mirrors are more common in household applications.