Hello Ansuman,
To get the offset voltage, we need to use the Ohm's Law in conjunction with the Superposition Theorem to determine the output voltage produced by the bias currents. First, the non inverting bias current will cause a voltage drop across RF with a value of
VRf = Ib2 x Rf
This voltage will be amplified by the non inverting gain of the amplifier and appear in the output as
Vo2 = VRf (1+Rf/R1) = Ib2 R3(1+Rf/R1)
Now let us consider the effect of the bias current for the inverting input. According to the Superposition Theorem, we must set the bias current on the non inverting input to 0. Having done this, we see that since no current is flowing through R3 there will be no voltage across it. Therefore, the voltage on the (+) input will be truly 0 or ground. Additionally, we know that the closed-loop action of the amplifier will force the inverting pin to be at a similar potential. This means that the inverting pin is also at ground potential. In any case, with 0 volts across R1 there can be no current flow through R1. The entire bias current for the inverting input, then, must flow through Rf (by Kirchhoff's Current Law). Since the left end of Rf is grounded and the right end is connected to the output, the voltage across Rf is equal to the output voltage. Therefore, the output voltage caused by the bias current on the inverting pin can be computed as
Vo1 = Ib1 x Rf
Now, continuing with the application of the Superposition Theorem, we simply combine (algebraically) the individual voltages computer above to determine the net effect of the two bias currents. Since the polarities of the output voltage caused by the two bias currents are opposite, the net output voltage must be
Vo = Vo1 - Vo2
Vo = Ib1 Rf - Ib2 R3(1+Rf/R1)
