Solve the Problem $L$ Of an Optical Telescope with Lens Diameter $D$

question 77

Multiple Choice

Solve the problem.
-The limiting magnitude $L$ of an optical telescope with lens diameter $D$ (in inches) is given by $L ( D ) =$ $8.8 + 5.1 \log D$ .
a. Find the limiting magnitude for a telescope with a lens 11 in. in diameter. Round to 1 decimal
b. Find the lens diameter of a telescope whose limiting magnitude is 10.7. Round to the nearest $\mathrm { i }$

• A) a. \(14.1\)
• B) a. \(5.3\)
• C) a. \(2.4\)
• D) a. 21
• b. \(2 \mathrm { in }\).
• b. 2 in.
• b. 14 in.
• b. 1 in. .

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Definitions:

Producer Surplus

The difference between what producers are willing to accept for a good versus what they actually receive, often due to higher market prices.

Underproduction

The situation where the production of goods or services is below an optimal level or capacity, often leading to shortages.

Nonexcludability

A characteristic of goods or services that makes it impossible to prevent people from consuming or using them, regardless of whether they have paid for them or not.

Free-Riding

The practice of benefitting from a good or service without paying for it or contributing to its provision, often discussed in the context of public goods.