Explanation Write the formula of Wien’s law. T 2 T 1 = λ p 1 λ p 2 (I) Here, λ p is the peak wavelength and T is the temperature. Write the formula for power output of stars by Stefan-Boltzmann. P = β A T 4 (II) Here, P is the power output, β is a constant, A is the surface area of the emitter. Write the formula of brightness. b = L 4 π d Here, b is the brightness, L is the lepton number and d is the distance. Compare the brightness of two stars. b 1 b 2 = ( L 1 4 π d 1 2 ) ( L 2 4 π d 2 2 ) (III) Substitute 0.091 for b 1 b 2 in equation (III) to calculate the ratio of brightness. 0.091 = ( L 1 4 π d 1 2 ) ( L 2 4 π d 2 2 ) d 2 2 d 1 2 = 0.091 L 2 L 1 (IV) By Stefan-Boltzmann law, power is same as the luminosity. Substitute L for P in equation (IV) to calculate the ratio of the distance. d 2 2 d 1 2 = 0.091 P 2 P 1 Here, P is the power. Substitute β A 1 T 1 4 for P 1 and β A 2 T 2 4 for P 2 in the above equation. d 2 2 d 1 2 = 0.091 β A 2 T 2 4 β A 1 T 1 4 = 0.091 A 2 T 2 4 A 1 T 1 4 Substitute 4 π r 1 2 for A 1 and 4 π r 2 2 for A 2 in the above equation

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