In a laboratory, a laser beam is split into two beams by a thin glass plate…

In a laboratory, a laser beam is split into two beams by a thin glass plate. The two beams are sent along different paths and made to cross on a screen. Because they come from the same laser, they are coherent. One path loses more light than the other, so the two beams reach the screen with unequal strength. Each beam alone would light the screen with an intensity of $6.25\ \text{W/m}^2$ and $1.00\ \text{W/m}^2$. Together they make a pattern of bright and dark places. The student has measured the strength of each beam with a light meter. She wants to know how clear the dark places of the pattern will be. She also wants to know how unequal two beams may be if the brightest place is to be a great many times as bright as the darkest. Find the greatest and the least intensity in the pattern, and the intensity where the phase difference is $90^\circ$. Find the visibility of the fringes, which is $\dfrac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}}$. Then find the ratio of the intensities of two beams for which $I_{\max}/I_{\min} = 49$.