A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment. (a) Find the distance of the third bright fringe on the screen from the central maximum for wavelength 650 nm. (b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?
The distance of the third bright fringe from the central maximum for wavelength 650 nm is 9.75 mm.
The least distance from the central maximum where bright fringes due to both wavelengths coincide is 13 mm.
Explanation
This numerical problem applies the fringe position formula from Young's double-slit experiment. The context provides the formula for bright fringe position: x = nλD/d. For part (a), we substitute n=3 for the third bright fringe. For part (b), we set the fringe positions equal for both wavelengths and find the smallest integers satisfying the ratio. Note: The values D=1.4 m and d=0.28 mm from Question 10.4 in the context are standard parameters used for this problem series.