A good hat and quality polaroid shades are going to make your fly fishing more comfortable, enjoyable and effective. Why? Both provide protection from stray flies, shield your eyes from light and help you locate feeding fish!
Having said that, getting the right combination takes more thought than grabbing the first glasses and baseball cap that comes to hand.
First, lets consider glasses. Without a doubt glass lenses rule. Their are some very good plastic lenses on the market, however they don’t compare with top spec glass lenses, buy the very best you can afford.
For freshwater fishing, amber/brown lenses are the best colour for providing you with top visibility in a range of light/water conditions. Make sure the glasses you choose are wrap around style, fitting snug to your face. This helps prevent unfiltered light entering your eye, enhancing your vision.
Looking at hats, my personal preference is for a long billed cap. The main point here is light being prevented from entering the eye over the top of your polaroid shades.
Hat colour is important too. Say you are quietly stalking along a bank. The one part of you moving most is your head as you scout for fish. A brightly coloured hat won’t spook fish itself, however movement of your head will be noticed easier and more light will be reflected on sunny days. This certainly will spook nearby fish!
If muted colours are important on the outside of your hat, a dark under brim is essential. Light colours reflect more light, dark colours absorb more light. So having that dark under brim minimizes light reflected back into your eyes from the hat’s brim. This makes a huge difference to your underwater vision, resulting in you spotting more fish and catching more fish.