A man is Standing on the peak of a mountain and finds that evening sun rays are nearly horizontal. At a horizontal distance of 6 km from him, its raining and he sees a beautiful rainbow. The sun rays entering water drop get refracted, reflected and refracted to form a rainbow. The red light is emitted from a drop upto a maximum angle of `42°` with respect to the incident sunlight. In front of the man there is a flat valley at a depth of 0.5 km from the mountain peak. What fraction of the complete circular arc of the rainbow is visible to the man?

Answer

0.53