Please help with step by step answer A double-slit experiment is set up using re
ID: 1465123 • Letter: P
Question
Please help with step by step answer
A double-slit experiment is set up using red light ( = 724 nm). A first order bright fringe is seen at a given location on a screen. What wavelength of visible light (between 380 nm and 750 nm) would produce a dark fringe at the identical location on the screen?
= ?nm
2)
A new experiment is created with the screen at a distance of 2.1 m from the slits (with spacing 0.1 mm). What is the distance between the second order bright fringe of light with = 682 nm and the third order bright fringe of light with = 407 nm? (Give the absolute value of the smallest possible distance between these two fringes: the distance between bright fringes on the same side of the central bright fringe.)
|x| =?m
Explanation / Answer
A. = arcsin(m*lambda1/d), where m = 1
= arcsin(m2*lambda2/d)
Thus lambda2 = lambda1/m2 , where m2 = 0.5, 1.5, etc (until lambda is within the specified range)
m=1.5 works; lambda1/1.5 = 482.66 nm
B. is small enough that we can use the small-angle approximation for deflection y.
y =m*lambda*D/d
y1 = 0.0396775 m
y2 = 0.0348875 m
Distance = difference = 0.00479 m