Q:  What is the brightness of the double-star system, expressed
           in magnitudes?


         The single star has magnitude = 3.  So, we need to find the 
         difference in magnitudes between single and double star,
         and add it to 3.



                                                   intensity(double)
          m(double) - m(single)  =   -2.5 log10 ( ------------------ )
                                                   intensity(single)


                                                   2
                                 =   -2.5 log10 ( ---- )
                                                   1


                                 =   -2.5 ( 0.301 )  =  -0.75


          Therefore,

                 magnitude of double    =   magnitude of single  -  0.75

                                        =       3  -  0.75
 
                                        =         2.25


          After a few years in the business, one starts to memorize
          the difference of -0.75 magnitudes for an object which is
          twice as bright.