A source $S_1$ is producing ${10}^{15}$ photons per second of wavelength $5000 \AA .$ Another source $S_2$ is producing $1.02 \times {10}^{15}$ photons per second of wavelength $5100 \AA .$ Then, $\frac{(power of S_2) }{(power of S_1)}$ is equal to:

For a source $S_1,$ Wavelength, ${\lambda }_1 = 5000 \AA$

Number of photons emitted per second, $N_1 ={10}^{15}$

Energy of each photon, $E_1 =\frac{hc}{{\lambda }_1}$

Power of source $S_1, P_1 = E_1{N}_1=\frac{N_{1}hc}{{\lambda }_1}$

For a source $S_2,$ Wavelength, ${\lambda }_2 = 5100 \AA$

Number of photons emitted per second, $N_2 = 1.02 \times {10}^{15}$ 

Energy of each photon, $E_2 =\frac{hc}{{\lambda }_2}$

Power of source $S_2, P_2 = N_2{E}_2=\frac{N_{2}hc}{{\lambda }_2}$

$\therefore \frac{Power of sources S_2}{Power of sources S_1}=\frac{P_2}{P_1}=\frac{\frac{N_{2}hc}{{\lambda }_2}}{\frac{N_{1}hc}{{\lambda }_1}}=\frac{N_2{\lambda }_1}{N_1{\lambda }_2}$

$=\frac{\left(1.02 \times {10}^{15} photons/s\right) \times \left(5000 \times {10}^{-10}\right)}{\left({10}^{15} photons/s\right) \times \left(5100 \times {10}^{-10}\right)}=\frac{51}{51}=1$