Question

Consider a source of light with wavelength λ = 490 nm that shines on two identical narrow slits. The slits are separated by a distance a = 30 μm. An interference pattern is observed on a screen located a distance L away from the slits. On the screen, the location of the second dark spot to the left of the central bright spot is found to be y = 1.2 cm from the central bright spot. Let this particular position on the screen be referred to as P₁.

A. Light from both slits travels to the point P₁. How much further does the light from one slit travel compared to the light from the other slit?
distance =     nm

B. The path difference in part A is equal to a·sinθ where the angle θ is the separation between the central bright spot and the second dark spot. What is this angle θ?
θ = °

C. Using the angle θ and the location y of the second dark spot on the screen, determine the distance L between the slits and the screen.
L =      m

Answer 1

A) for second dark spot the path diffrence = (3/2)*lamda

= (3/2)*490

= 735 nm <<<<<<<<<<<<-----------------Answer

B) a*sin(theta) = (3/2)*lamda

30*10^-6*sin(theta) = 735*10^-9

sin(theta) = 735*10^-9/(30*10^-6)

sin(theta) = 0.0245

theta = sin^-1(0.0245)

= 1.40 degrees <<<<<<<<<<<<-----------------Answer

C) tan(theta) = y/L

==> L = y/tan(theta)

= 1.2/tan(1.40)

= 49.1 cm

= 0.491 m <<<<<<<<<<<<-----------------Answer