SOLUTION: An optical instrument with limiting magnitude L of any optical telescope and lens
diameter D, in inches, is given by
𝐿 = 8.8 + 5.1 𝑙𝑜𝑔 𝐷
a) Determine the limiting
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-> SOLUTION: An optical instrument with limiting magnitude L of any optical telescope and lens
diameter D, in inches, is given by
𝐿 = 8.8 + 5.1 𝑙𝑜𝑔 𝐷
a) Determine the limiting
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Question 1198664: An optical instrument with limiting magnitude L of any optical telescope and lens
diameter D, in inches, is given by
𝐿 = 8.8 + 5.1 𝑙𝑜𝑔 𝐷
a) Determine the limiting magnitude for a homemade I -inch reflecting telescope.
b) Determine the diameter of a lens that would have a limiting magnitude of R.
You can put this solution on YOUR website! **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).
