A Young's double slit has a slit separation of 2.50 x 10^-5 m on which a monochromatic light beam is directed.The resultant bright fringes on a screen 1.00 m from the double slit are separated by 2.30 x 10^-2m.What is the wavelength of this beam? (1 nm = 10^-9 m)

Question

Quizplus · Accepted Answer

We can use the formula for the distance between two adjacent bright fringes:
d*sin(θ) = mλ
where d is the slit separation, θ is the angle between the line connecting the center of the double slit and the fringe and the normal to the screen, m is the order number of the fringe, and λ is the wavelength of the light.

In this case, we can assume that the screen is far enough from the double slit that θ is small and can be approximated by θ = y/L, where y is the distance between the central maximum and the mth bright fringe on the screen, and L is the distance between the double slit and the screen.

Substituting the given values, we get:

2.30 x 10^-2 m = (1)(575 x 10^-9 m)*(1.00 m)/(2.50 x 10^-5 m)

Solving for λ, we get:

λ = (2.30 x 10^-2 m)(2.50 x 10^-5 m)/(1.00 m) = 575 x 10^-9 m = 575 nm

Therefore, the answer is choice C.

A Young's Double Slit Has a Slit Separation of 2