Question

Two very narrow slits are spaced 1.85 μm and are placed 30.0 cm from a screen.

What is the distance between the first and second dark lines of the interference pattern when the slits are illuminated with coherent light with a wavelength of 546 nm ? (Hint: The angle θ in equation dsinθ=(m+12)λ is not small.)

Answer 1

d = 1.85 um = 1.85 x 10^-6 m

D = 30 cm = 0.3 m

wavelength = lamda = 546 nm = 546 x 10^-9 m

d sin(theta1) = lamda / 2

d sin(theta2) = 3 lamda / 2

theta1 = arcsin( 0.5 lamda / d ) = arcsin( 0.5 * 546*10^-9 / (1.85*10^-6) ) = 0.148 rad

theta2 = arcsin( 1.5 lamda / d ) = arcsin( 1.5 * 546*10^-9 / (1.85*10^-6) ) = 0.458 rad

Distance between 1st and 2nd dark interference patterns = y1 = y2 = D( tan(theta2) - tan(theta1)

= 0.3 * ( tan(0.458) - tan(0.148) ) = 0.103 m = 10.3 cm