How do I know if concentration of Ammonia affected my absorbency measurements?
The concentration of ammonia will matter, but only up to a certain point. 

When you dissolve copper in nitric acid, you form copper nitrate, which is very soluble, but as you say, not very absorptive.

$$\ce{Cu(s) +2HNO3(aq) -&gt; Cu(NO3)2(aq)+H2(g)}$$

One of the problems with copper nitrate is that it dissociates readily in water.

$$\ce{Cu(NO3)2(aq) -&gt; Cu^{2+}(aq) + 2NO3^{-}(aq)}$$

The copper(II) ions then coordinate with varying amounts of water molecules. Each balue of $\ce{x}$ in the equation below is a slightly different aqua complex with slightly different optical properties.

$$\ce{Cu^{2+}(aq) +xH2O-&gt; Cu(H2O)_{x}^{2+}(aq)}$$

The addition of ammonia changes the situation. Ammonia binds strongly to copper to preferentially form the tetraamminecopper(II) complex, technically $\ce{Cu(NH3)4(H2O)2^{2+}}$, which is highly absorptive. Since this formation is highly favored, you only need to add enough ammonia to provide at least 4 stoichiometric equivalents.

If the ammonia solution you added was labeled "Ammonium Hydroxide" (as you say in your question), then you know how much ammonia you added. Your instructor just might not have told you how to do it.

Ammonium hydroxide exists only by the ionization of ammonia in water (which is very small except at high concentrations). Labeling a solution as "Ammonium Hydroxide" has come to mean a "saturated solution of ammonia in water", which is 35% ammonia by mass (approx. 18 molar). Now you can calculate the amount of ammonia that you added (as long as you know the volume of solution that you added).

To determine the effect of amount of ammonia, you can do the following:


  Dilute the original ammonium hydroxide solution. For example, dilute 25 mL of the solution to 50 mL with water to get an ammonia solution of about 9 molar. Then repeat the penny experiment and add exactly the same volume of the new ammonia solution. This guarantees that the overall copper concentration remains constant even when the ammonia concentration changes. Then measure the absorbance. Then dilute the ammonia solution again (either dilute the new solution or dilute the original solution by a different amount). Rinse and repeat.