A refracting telescope has an objective lens of focal length 80 cm, a diameter of 10 cm, and an eyepiece of focal length 5 cm and diameter 1 cm. How much more light will this telescope collect than the average unaided eye, whose focal length is 2 cm and diameter is 0.5 cm?

Question

Quizplus · Accepted Answer

First, we can find the ratio of the light collecting abilities of the two telescopes (using the formula $A=\pi r^2$, where $r$ is the radius or half the diameter):
$$\frac{A_{	ext{telescope}}}{A_{	ext{eye}}}=\frac{\pi(\frac{10}{2})^2}{\pi(\frac{0.5}{2})^2}=1600$$
So, the telescope collects 1600 times more light than the unaided eye.

Second, we can find the ratio of the amount of light that reaches the eyepieces of the two telescopes:
$$\frac{f_{	ext{telescope}}}{f_{	ext{eye}}}=\frac{80}{5}=16$$
So, the telescope focuses 16 times more light onto the eyepiece than the unaided eye.

Multiplying these two ratios gives us the total amount of light that reaches the eyepiece of the telescope compared to the unaided eye:
$$1600	imes 16=25600$$
Therefore, the telescope collects 25,600 times more light than the unaided eye.

A Refracting Telescope Has an Objective Lens of Focal Length