The problem is that my sensor (mini solar panel) reads max value under little light and does not go beyond that level no matter how much light falls onto it in the later stage.
Open voltage is not a good way to read the light level hitting a solar panel in this situation. Much better is to measure the current generated by the solar cell by adding a resistor across it here...
The value of the resistor can be found using...
V=IR
... where ...
V=1.1 volts
I=the maximum current the solar cell can generate in full light
If you do this, then you can read the A1 pin using the 1.1V ref and you will be able to measure the full range of light conditions using the solar cell with simple Arduino code like this..
analogReference(INTERNAL); // a built-in reference, equal to 1.1 volts
int v=analogRead(A1); // Returns value 0-1023 representing light level
PS: Note if you measure the battery voltage with a divider as shown, you will be drawing current (about 0.8 milliamps when the battery reaches its minimum voltage) ALL THE TIME - even when the circuit is off. You do not want to do this with a lithium battery since under-voltaging it can potentially cause permanent damage to it. You really should heed my answer to your other question here.
PPS: It is usually best to ask your real question directly rather than asking a bunch of questions that are synthetic and reflect problems you think you have rather than the problems you actually do have. Your supplied code and drawings should match the thing you are asking and the thing you are actually working on (and each other!). It is often the case that the problem is not where you think it is, and so showing code and drawings that do not reflect what is really going on just wastes people's effort and does not ultimately help you solve your real problem. :)