We have LED at the output of 40 watts and is used for 0 hours giving us 400 Watts-hr of energy consumed.Rechargable batteries needed are 2 V. 400/2 gives us 34 Ampere-hour battery needed. If we want it for 3 days, It would be 34x3=00 Ah. So the battery needed 00 AhNow how do I select the solar panel which can charge this/these batteries? What should be its rating?
Be aware that you cannot discharge the full capacity of a lead-acid battery without destroying the battery. With a normal battery of this type, you would only want to discharge about 20%, so you would need a 70 AH battery bank. For the 3-day requirement, 500 AH. This is still within reason. If you didn't have the 3-day requirement, you might consider going with NiMH batteries. Back to the 500 AH bank, you would usually charge at at least 5% C, or 25 amps. At the 5 volts that you need for charging, this is 375 watts. Possibly you could go as low as 200 watts.
First, you need to make sure that your battery can take a regular 34Ah discharge without damage. The usual wisdom when using deep cycle lead-acid batteries is to allow for no greater than 50% discharge. This is to prevent the battery from ageing prematurely. Note that automotive batteries are not usually considered suitable for deep-cycle applications. Best allow for at least 200Ah capacity. Your solar panel capacity needs to take into account that whatever the nameplate output of the panel, that will be what it will produce under ideal conditions, actual output will always be less, often quite a bit less. You also need to allow capacity to cope with dull, overcast days when the light level is very low. You can get solar maps that will give you the sunshine hours and irradiation levels at your location. The solar panel capacity ends up being a juggling act between available funds/space and how critical it is that the light always works as desired. Let's say you had a 400W panel, which sounds quite generous. In the middle of winter, it may produce only 75W for 5 hours on a dull day, not quite enough to run the light for 0 hours. Would you expect several such days in a row? How many days could a 00Ah of battery capacity cover under these conditions?
