How did Brian catch the fish in Hatchet?

Brian tried for a long time to catch fish.  He tried using a spear and a bow at different times too.  After being stranded in the wilderness for 47 days, Brian has had plenty of trial and error experiences with surviving.  He had luck with small birds and berries, but fish were a tough prey to capture.  In chapter 13 Brian recounts his first success at putting an arrow through a fish.  

Finally, after hours, he stuck the arrow down in the water, pulled the bow, and waited for a fish to come close and while he was waiting he noticed that the water seemed to make the arrow bend or break in the middle.

Of course—he had forgotten that water refracts, bends light. He had learned that somewhere, in some class, maybe it was biology—he couldn't remember. But it did bend light and that meant the fish were not where they appeared to be. They were lower, just below, which meant he had to aim just under them.

Brian finally was able to spear his first fish with an arrow because he relearned a valuable physics lesson about light.  Water refracts (bends) light. Water is a denser substance than air, so water slows light down.  Because light is a wave, different parts of the wave exit the water at different times.  This causes the light to bend, which makes objects in the water appear to be in locations where they are not.  Brian adjusted his aim to below the fish, which is not where the fish appeared to be, but it is where the fish actually was.    

In Hatchet, what action of Brian's attracted the fish?

Gary Paulsen's 1987 novel Hatchet tells the story of a thirteen-year-old-boy, Brian Robeson, and his journey to survive in the wild. While on a small passenger plane with only himself and the pilot, Brian is thrown into a life and death battle after the pilot suffers a heart attack and the plane crashes. The only survivor, Brian is stranded in the deep wilderness of northern Canada and must learn to use his hatchet, a gift from his mother, to survive on his own in the wild.

Brian's plane crashed near a lake, and he quickly becomes determined to figure out how to catch some fish. He tries several methods. First, he wades into the water and stands very still and then tries to catch a fish by hand. When that is unsuccessful, he decides that he needs to create a wooden spear with two prongs at its end to capture the fish. However, this method also does not work.

Finally, Brian realizes that he can finally become faster than the fish if he creates a bow and arrow specifically for catching fish. Using his hatchet, he creates a small wooden bow and then crafts wooden arrows out of willow branches, shaping their ends into points and prongs. When Brian tests his new invention, he is at first unsuccessful. However, he suddenly realizes his mistake.

Of course—he had forgotten that water refracts, bends light. He had learned that somewhere, in some class, maybe it was biology—he couldn’t remember. But it did bend light and that meant the fish were not where they appeared to be. They were lower, just below, which meant he had to aim just under them. He would not forget his first hit. Not ever. A round-shaped fish, with golden sides, sides as gold as the sun, stopped in front of the arrow and he aimed just beneath it, at the bottom edge of the fish, and released the arrow and there was a bright flurry, a splash of gold in the water. He grabbed the arrow and raised it up and the fish was on the end, wiggling against the blue sky. He held the fish against the sky until it stopped wiggling, held it and looked to the sky and felt his throat tighten, swell, and fill with pride at what he had done. He had done food. With his bow, with an arrow fashioned by his own hands he had done food, had found a way to live.

Later, Brian learns that he can section of part of the river to create pond for luring fish into with bait. The fish swim into the pond and into a fine mesh net that Brian has created by weaving fine willow branches together.

Storing live fish to eat later had been a major breakthrough, he thought. It wasn’t just keeping from starving—it was trying to save ahead, think ahead. Of course he didn’t know then how sick he would get of fish.

In Hatchet, what was Brian's next idea for catching fish after his initial failure?

Brian struggles for food sources.  He realizes that catching fish in the L Shaped Lake could help him with this.  His original attempt was to make a spear and use it to catch the fish.  This was a good idea, but failed because of the refraction of life and the fact that its single tip proved to allow fish to escape.  In order for Brian to be more successful, he aimed his speak taking the bending of light into account and then also created a double tipped spear.  This allowed him to be more precise with his aim and catch more fish for a plentiful food source.  This instance proves that Brian learned the element of persistence and mental toughness in that there is little fear of failure.  He understands that there is little other choice than to fight through these setbacks and focus on what he needs in order to survive.