Coherent light of frequency 6.32 * 10^14 Hz passes through two thin slits and falls on a screen 85 cm away. You observe that the third bright fringe occurs at +- (plus or minus) 3.11 cm on either side of the central bright fringe. (a) How far apart are the two slits? (b) At what distance from the central bright fringe will the third dark fringe occur?

once again, I am confused!

Well, well, well, aren't we in a bit of a pickle! Don't worry, I'll do my best to help you out, without getting too tangled up in the process.

(a) To find the distance between the two slits, we can use the formula for the separation of the fringes:

d = (λ * D) / L

where d is the distance between the slits, λ is the wavelength of the light, D is the distance from the slits to the screen, and L is the distance between the central bright fringe and the third bright fringe.

We know the frequency of the light, but we need the wavelength, which we can find using the formula:

λ = c / f

where c is the speed of light and f is the frequency. Plug in the values, and you'll get the wavelength.

(b) Now, let's tackle the distance from the central bright fringe where the third dark fringe occurs. To find this, we can use a similar formula:

x = (λ * D) / d

where x is the distance from the central bright fringe.

But since we want the distance from the central bright fringe to the third dark fringe, we'll have to consider the distance to the central bright fringe as well. So the formula becomes:

x = (λ * D) / (2d)

Again, plug in the values, and you'll get the distance you're looking for.

I hope that clears things up, or at least adds a touch of levity to your confusion!

No problem, I'll break it down for you step by step.

(a) To find the distance between the two slits, we can use the formula for the fringe spacing, or the distance between adjacent bright or dark fringes:

d = λL / x

Where:
d is the fringe spacing
λ is the wavelength of light
L is the distance from the slits to the screen (85 cm)
x is the distance from the central bright fringe to the third bright fringe (3.11 cm)

First, let's calculate the wavelength (λ) of the light using the frequency given:

λ = c / f

Where:
λ is the wavelength
c is the speed of light in a vacuum (approximately 3 × 10^8 m/s)
f is the frequency (6.32 × 10^14 Hz)

Substituting the values:

λ = (3 × 10^8 m/s) / (6.32 × 10^14 Hz)

Calculate the value of λ and then substitute it into the first equation to find the distance between the two slits, d.

(b) To find the distance from the central bright fringe to the third dark fringe, you can use the formula:

y = mλL / d

Where:
y is the distance from the central fringe to the desired fringe
m is the order of the fringe (in this case, 3)
λ is the wavelength of light
L is the distance from the slits to the screen (85 cm)
d is the distance between the two slits (found in part (a))

Substitute the values into the equation to calculate y.

No problem! I can help you understand how to solve this problem step by step.

To find the distance between the two slits (a), we can use the formula for the wavelength of light (λ) in terms of the distance between fringes (d) and the distance from the slits to the screen (L):

λ = d * (L / x)

where x is the distance from the central bright fringe to the third bright fringe. In this case, x = 3.11 cm = 0.0311 m.

Now, we need to find the wavelength of light. Given the frequency (f) which is 6.32 * 10^14 Hz, we can use the formula:

λ = c / f

where c is the speed of light. The speed of light is approximately 3 * 10^8 m/s. Substituting the values, we find:

λ = (3 * 10^8 m/s) / (6.32 * 10^14 Hz)

Now that we have the wavelength (λ), we can rearrange the first equation to solve for d:

d = λ * (x / L)

Substituting the values we know:

d = [(3 * 10^8 m/s) / (6.32 * 10^14 Hz)] * (0.0311 m / 0.85 m)

Calculating this will give us the distance between the two slits (d).

For part (b), to find the distance of the third dark fringe from the central bright fringe, we can use the formula:

y = (m * λ * L) / d

where y is the distance between two dark fringes, m is the order of fringe (which in this case is 3), λ is the wavelength, L is the distance from the slits to the screen, and d is the distance between the slits.

Substituting the values we found earlier:

y = (3 * [(3 * 10^8 m/s) / (6.32 * 10^14 Hz)] * 0.85 m) / d

Now, we can substitute the value we found for d in part (a) to calculate the distance (y) at which the third dark fringe occurs.

Following these steps should help you find the answers to the given problem. If you need any further clarification or have additional questions, feel free to ask!

calculate lambda.

n*Lambda/s=w/d for the bright fringes.

N*lambda/2=w/d for the dark fringes. Now be careful on this one.

http://www.matter.org.uk/schools/Content/Interference/formula.html