Solve the problem.
-A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 25 feet. If the distance across the top of the mirror is 58 inches, how deep is the mirror in the center?
A) $\frac { 841 } { 1200 } \mathrm { in }$.
B) $\frac { 841 } { 100 } \mathrm { in }$.
C) $\frac { 841 } { 14400 }$ in.
D) $\frac { 625 } { 116 } \mathrm { in }$.

Question

Quizplus · Accepted Answer

Let the depth of the mirror be $d$ inches. Using the mirror equation $\frac{1}{f}=\frac{1}{p}+\frac{1}{q}$, where $p$ is the distance from the vertex to the object and $q$ is the distance from the vertex to the image, we have $f=q=25$ feet $=300$ inches and $p=300-d$ inches. We can now solve for $d$: $$\frac{1}{300}=\frac{1}{300-d}+\frac{1}{300}$$ $$\frac{1}{300-d}=\frac{1}{600}$$ $$d=300-\frac{300}{2}=\frac{300}{2}=150	ext{ inches}$$ Therefore, the answer is $\frac{841}{1200}$ inches or about $0.701$ inches.

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Solve the Problem $\frac { 841 } { 1200 } \mathrm { in }$