The wave nature of light

In summary, the conversation discusses a double slit experiment with a slit separation of 2.0mm and two different wavelengths of light being used. The question asks at what distance on the screen will a bright fringe from one pattern align with a bright fringe from the other. The answer is 0.0045m, which is found by setting up a trigonometric equation and solving for m.
  • #1
Dx
Hello,

In a double slit experiment the slit separation is 2.0mm and two wavelengths 750nm and 900nm illuminate the slits. A screen placed 2m from the slits. at what distance from the central maximum on the screen will a bright fringe from one pattern first conincide with a bright fringe from the other?

my formula?
d = sin[the] / (m [lamb]

Is my answer correct 6.0mm

Thanks!
Dx :wink:
 
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  • #2
at what distance from the central maximum on the screen will a bright fringe from one pattern first conincide with a bright fringe from the other?
d=2E-3meters, λ1=750E-9m, λ2=900E-9m, D=2m (D being adjacent leg of right triangle, y1 and y2 being opposite legs, θ being angle between slits.)
y1 = mλ1D / d = (1)(750E-9m)(2m)/(2E-3)m = 7.5E-4m
y2 = nλ2D / d = (1)(900E-9m)(2m)/(2E-3)m = 9.0E-4m
were n=m=1, WHICH THEY're not.
You can't solve it trigonometrically.
In order to solve it, you need to equate
y1=y2=mλ1D/d = nλ2D/d
Then you just solve for m:
m = (λ2/λ1)n = 1.2n
The first instance of this relation being true is if m=6 and n=5
Now you just solve y1 and y2 above to get...

y1=y2=0.0045m
 
  • #3


Hello Dx,

Your answer is not quite correct. The formula you provided is the correct one to use, however, the value for "m" should be the same for both wavelengths since we are looking for the first bright fringe that coincides for both patterns. The value for "m" represents the order of the fringe, with m=0 being the central maximum. So, for the first bright fringe to coincide, we need to solve for m=1 for both wavelengths.

Using the given values, we get:

d = sin[the] / (m [lamb])

For 750nm:
d = sin[the] / (1 x 750nm)
d = sin[the] / 750nm

For 900nm:
d = sin[the] / (1 x 900nm)
d = sin[the] / 900nm

Since we are looking for the same distance, we can set these two equations equal to each other and solve for d:

sin[the] / 750nm = sin[the] / 900nm
Cross-multiplying and solving for d, we get:
d = (750nm x 900nm) / 750nm
d = 900nm

Therefore, the first bright fringe from one pattern will coincide with the first bright fringe from the other at a distance of 900nm from the central maximum on the screen.

I hope this helps clarify things. Keep up the good work!


 

1. What is the wave nature of light?

The wave nature of light refers to the fact that light exhibits properties of a wave, such as diffraction, interference, and polarization. This means that light can bend, overlap, and vibrate in different directions, similar to how a wave behaves in water.

2. How does light travel as a wave?

Light travels as a wave through the electromagnetic spectrum, which includes all forms of electromagnetic radiation. This includes visible light, as well as other forms of light such as radio waves, microwaves, and x-rays. These waves travel through space at the speed of light, which is approximately 299,792,458 meters per second.

3. How is the wave nature of light different from the particle nature?

The wave nature of light is different from the particle nature in that light can behave as both a wave and a particle, known as the wave-particle duality. When observed, light can act like a particle, but when not observed it behaves like a wave. This is known as the observer effect and is a fundamental principle of quantum mechanics.

4. What is the relationship between wavelength and frequency in light waves?

Wavelength and frequency are inversely related in light waves. This means that as the wavelength of a light wave increases, its frequency decreases, and vice versa. This relationship is described by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency.

5. How does the wave nature of light impact our daily lives?

The wave nature of light has a significant impact on our daily lives. Without it, we would not be able to see objects or colors, as light waves are responsible for our sense of vision. Additionally, many modern technologies, such as lasers, fiber optics, and wireless communication, rely on the properties of light waves and their ability to travel through space at high speeds.

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