Mathematical Modelling for Event Occurrence Rainbow Secondary

Secondary rainbow is a rainbow that formed because light is reflected twice when entering the rain drops and looks right out over the primary rainbow. Rules to formation of the secondary rainbow is same as the primary rainbow when it rains coincide with the sun shining from the other side and the observer is between them. The aims of research are: determine the mathematical model of the secondary rainbow, determine the angle, and the angle secondary rainbow colors using differential calculus. This observation method using literature study which is based on the theoretical framework underlying the ways of solving the problems that include, derivatives, maximum/minimum value, and the properties of light. The results of this research is deviation angle of the mathematical models secondary rainbow; D S   =   2 θ 1 − 6 ( sin − 1 ( n u sin θ 1 n a ) ) + 2 π . This model found the optimum angle of the I V n a )) secondary rainbow is 51 °. Large corner secondary rainbow of colors Red, Orange, Yellow, Green, Blue, Indigo and Violet are respectively 50.57, 51.12, 51.72, 52.42, 52.78, 53.45 and 53.60 (in degrees). It is shown that large rainbow angle for each colors of secondary rainbow are different, it is explains that the secondary rainbow is composed of seven colors.