Question

Suppose you want to make an interferometer with two slits to show the wave nature of light to your friends. The most convenient bright light is the Sun, so you find a long cardboard box that you can take outside. The box will make a dark space in which you can make the beams through the slits combine into a pattern, and have it visible to someone looking into the box. There is a video of it this on the class site this week. Let the slits be 1 mm apart, and the box 1.5 meters long from the end where the slits are to the bottom where a white piece of paper will show the pattern.
a. Is the center of the pattern bright or dark?
b. How far is it in mm from the center of the pattern to the tenth bright fringe on either side with green light of wavelength 550 nm?
c. The fringes will show color. What is the ordering of the color from the center out, i.e. red green blue, blue green red, or something else?
d. If you did not know anything about the wavelength of light, how would you use the double slit to find the wavelength of red light?

Answer 1

Answer:

a) the pattern is bright,  b)  y = 8.25 mm, c) the distance increases with the wavelength increases

Explanation:

This is a team building exercise to perform interference experiments, where the separation of the slits is d = 1 m = 1 10⁻³ m and the distance to the screen L = 1.5 m  

Constructive interference occurs when the path difference is equal to an integer number of wavelengths  

             d sin θ = m λ  

a) The center of the two-ray pattern has the same length so the intensity is MAXIMUM, that is, the pattern is bright  

b) to find the distance let's use trigonometry  

   tan θ= y / L  

   tan θ =sin θ/cos θ= sin θ  

because the angles are small  

we substitute  

     y = $\frac{m \lambda L}{d}$ 

let's calculate  

     y = 10 550 10⁻⁹ 1.5 / 1 10⁻³  

     y = 8.25 10⁻³ m

c) for this part the incident light must be white or polychrome light  

let's find the distance (y) for some colors, in the first order  

Violet λ = 400  

y = 1 400 10⁻⁹ 1.5 / 1 10⁻³  

y = 6 10⁻⁴ m  

green λ = 500 nm  

y = 1 500 10⁻⁹ 1.5 / 1 10⁻³  

y = 7.5 10⁻⁴ m  

yellow λ = 600 nm  

y = 1 600 10⁻⁹ 1.5 / 1.10⁻³  

y = 9 10⁻⁴ m  

lam λ = 700 nm  

y = 1 700 10⁻⁹ 1.5 / 1. 10⁻³  

y = 1.05 10⁻³ m  

violet, green, orange, red  

the distance increases with the wavelength increases

d) To find the wavelength we must measure the distance y from the center of the slit for various interference orders and using the equation we can find the wavelength of rationality