Solution Found!
When using a telescope to photograph a faint astronomical
Chapter 27, Problem 98GP(choose chapter or problem)
Problem 98GP
When using a telescope to photograph a faint astronomical object, you need to maximize the amount of light energy that falls on each square millimeter of the image on the film. For a given telescope and object, the total light that falls on the film is proportional to the length of the exposure, so a long exposure will reveal fainter objects than a short exposure. Show that for a given length of exposure, the brightness of the image is inversely proportional to the square of the f-number of the telescope system.
Questions & Answers
QUESTION:
Problem 98GP
When using a telescope to photograph a faint astronomical object, you need to maximize the amount of light energy that falls on each square millimeter of the image on the film. For a given telescope and object, the total light that falls on the film is proportional to the length of the exposure, so a long exposure will reveal fainter objects than a short exposure. Show that for a given length of exposure, the brightness of the image is inversely proportional to the square of the f-number of the telescope system.
ANSWER:
Solution 98GP
Step 1 of 2
Here we need to prove that for the given length of exposure, the brightness of the image is inversely proportional to the square of the of the telescope system.
In the given case, the amount of light is directly proportional to the area.
That is,