A laser beam of wavelength 680 nm shines through a diffraction grating that has 750 lines/mm and observed on a screen 1.4 m behind the grating. How many bright fringes can be observed on a screen? Wha

The number of bright fringes that can be observed on the screen can be calculated using the formula: n? = m? where n is the number of lines per unit length on the diffraction grating, ? is the angle between the central maximum and the mth bright fringe, m is the order of the bright fringe, and ? is the wavelength of the laser beam. Rearranging the formula, we get: m = n? / ? Substituting the given values: n = 750 lines/mm = 750,000 lines/m ? = 680 nm = 0.68 ?m ? = sin?? (?/d), where d is the distance between adjacent lines on the grating For a diffraction grating with 750 lines/mm, the distance d between adjacent lines is: d = 1/750 mm = 1.333 ? 10?? mm = 1.333 ? 10?? m ? = sin?? (0.68 ? 10?? / 1.333 ? 10??) = 28.01° Substituting these values in the formula for m, we get: m = 750,000 ? 28.01° / (0.68 ? 10??) = 1,557,352.9 Since the order of the bright fringe should be a whole number, we round off the result to the nearest integer: m = 1,557,353 = 1.6 ? 10? (rounded off) Therefore, we can observe about 1.6 million bright fringes on the screen. The distance between two adjacent bright fringes of order m and m+1 can be calculated using the formula: ?y = ?L / d where L is the distance between the diffraction grating and the screen. Substituting the given values: ? = 0.68 ?m L = 1.4 m d = 1/750 mm = 1.333 ? 10?? m m = 1 ?y = (0.68 ? 10??) ? 1.4 / (1.333 ? 10??) = 0.714 mm Therefore, the distance between the two m = 1 fringes is 0.714 mm.