# Double Slit Homework: Order Max at 730 and 558 nm

• woaini
In summary: And what are the values for each of the two wavelengths?In summary, a double slit apparatus is illuminated with 730 nm and 558 nm wavelengths, forming a two-colored interference pattern at a distance of 2.28 m from the slits. The slit separation is 42 wavelengths of 730 nm light. Using the equations mλ=dsinθ and tanθ=y/L, the order of intensity maximum for λ=730 nm light near a distance of y=0.205 m away from the central zeroth order is approximately 4 or 5. For λ=558 nm light, the closest order maximum is also approximately 5.
woaini

## Homework Statement

A double slit apparatus is illuminated 730 and 558 nm wavelengths. They form a two-colored interference pattern on a measuring screen located at a distance of 2.28 m from the slits. The slit separation is 42 wavelengths of 730 nm light.
(a) What order (m) intensity maximum for λ = 730 nm light occurs near a distance of y = 0.205 m away from the central zeroth order?
(b) What order maximum for 558 nm light lies closest to this order?

λ1=730
λ2=558
L=2.28
m=?
d=42*730

mλ=dsinθ
tanθ=y/L

## The Attempt at a Solution

tanθ=.205/2.28 θ=5.14

a) m=(dsinθ)/λ = 3.76 (4?)

a) m=(dsinθ)/λ = 4.92 (5?)

So did I get the slit separation right? Are my orders suppose to be decimal numbers and do I round up or down?

Your working for a) looks right, but it bothers me that it's not closer to a whole number. Doesn't strike me as particularly 'near'. As a check, I adjusted for the fact that d/D is really tan(theta), but it made hardly difference.
For b), although it's worded a little oddly, I think it's asking which order of 558nm max is nearest the 730nm max you just identified. Note that this not quite the same as asking which order of 558nm max is nearest 0.205m from the central axis. (But it still gives 5 as the answer.)

So if it's near the 4th order, I would do this:

arcsin((4*750)/(42*730)) = 5.61

L*tan(5.61)=0.224m
y2=0.224m

I'm lost here. :(

woaini said:
So if it's near the 4th order, I would do this:

arcsin((4*750)/(42*730)) = 5.61
You mean 4*730, right? so it reduces to 4/42. But it's much simpler than this.
Write out the mλ=dsinθ equation for the two different wavelengths. Which variables are the same between the two equations?

The dsin remain constant right?

woaini said:
The dsin remain constant right?
Yes, d and θ are constant. So what equation can you write for the rest?

## What is the purpose of the "Double Slit Homework: Order Max at 730 and 558 nm"?

The purpose of this homework is to apply the principles of the double slit experiment and use mathematical calculations to determine the maximum order for light at two different wavelengths, 730 nm and 558 nm.

## What is the double slit experiment?

The double slit experiment is a classic experiment in physics that demonstrates the wave-like nature of light. It involves passing a beam of light through two parallel slits and observing the interference pattern created on a screen behind the slits.

## Why is it important to determine the maximum order for light at specific wavelengths?

Knowing the maximum order for light at specific wavelengths allows us to understand the behavior of light and its interference patterns. It also helps us to make predictions and perform calculations in various applications, such as diffraction grating and spectroscopy.

## What factors affect the maximum order for light at specific wavelengths?

The maximum order for light at specific wavelengths is affected by the distance between the slits, the distance from the slits to the screen, the wavelength of the light, and the angle at which the light is diffracted.

## How can the maximum order for light at specific wavelengths be calculated?

The maximum order for light at specific wavelengths can be calculated using the formula: m = (d sin θ)/λ, where m is the order, d is the distance between the slits, θ is the angle of diffraction, and λ is the wavelength of light.

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