Answer to Question #202445 in Optics for Sunny Khan

Question

a) A viewing screen is separated from a double-slit source by 2 m. The distance between

the two slits is 0.06 mm. The fifth-order bright fringe is 15 cm from the center line. (a) Determine

the wavelength of the light. (b) Calculate the distance between adjacent bright fringes.

Answer 1

For bright fringe

dsinθ=mλ

θ= angle between observer line to center and fringe

d = distance between the center of slits

d=0.06 mm

L=D=2 m (separation of the screen)

$sinθ = \frac{y}{L}$

(a)

$d \times \frac{y}{L}=mλ$

m=5

y=15 cm

$0.06 \times 10^{-3}\;m \times \frac{0.15 \;m}{2\;m}=5λ \\ λ = 9 \times 10^{-7} \;m$

(b)

m=1

$d \times \frac{y}{L}=λ \\ y = \frac{λL}{d} \\ = \frac{9 \times 10^{-7} \times 2}{0.06 \times 10^{-3}} \\ =0.03 \;m = 3 \;cm$