Question 1198664
**a) Determine the limiting magnitude for a homemade 1-inch reflecting telescope.**

* Use the given formula: L = 8.8 + 5.1 * log(D) 
* Substitute D = 1 inch: 
   L = 8.8 + 5.1 * log(1)
* Since log(1) = 0:
   L = 8.8 + 5.1 * 0
   L = 8.8 

**Therefore, the limiting magnitude for a homemade 1-inch reflecting telescope is 8.8.**

**b) Determine the diameter of a lens that would have a limiting magnitude of R.**

* **Rearrange the formula to solve for D:**
    * L = 8.8 + 5.1 * log(D)
    * L - 8.8 = 5.1 * log(D)
    * (L - 8.8) / 5.1 = log(D)
    * 10^[(L - 8.8) / 5.1] = 10^(log(D))
    * 10^[(L - 8.8) / 5.1] = D

**Therefore, the diameter of a lens that would have a limiting magnitude of R is:**

* D = 10^[(R - 8.8) / 5.1] 
 
This equation allows you to calculate the required lens diameter for any desired limiting magnitude (R).