Wave Nature of Light - Calculating Wavelength (Double Slit Exp)

[PeachBanana]

Homework Statement

Monochromatic light falls on two very narrow slits 0.046 mm apart. Successive fringes on a screen 5.30 m away are 7.0 cm apart near the center of the pattern. Determine the wavelength of the light to two significant figures.

Homework Equations

x2 ≈ Lθ2 = L (2λ) / d

The Attempt at a Solution

I'm guessing the θ is very small so I can assume sin θ ≈ θ in radians. When the problem said the successive fringes were 7.0 cm apart near the center of the pattern, I thought that meant x2 was 7.0 cm above x1.

λ = dx2 / 2L
λ = (0.07 m)(4.6 *10^-5 m) / (2 * 5.30 m)
λ = 3.01 * 10^-7 m

 

[mfb]

I think there is a factor of 2 missing (or too much) somewhere. With the distance d between the slits, two adjacent fringes appear with an angle of $\alpha \approx \frac{\lambda}{d}$ between them.
In addition: With twice your calculated wavelength, the light is visible.

 

[PeachBanana]

I multiplied my answer by "2" and got it correct but I am still unsure why I should have multiplied by "2." Were you stating at 3.01 * 10 ^-7 m light is not visible?

 

[mfb]

That corresponds to 301nm - ultraviolet radiation.

but I am still unsure why I should have multiplied by "2."

I think you divided by 2, where you shouldn't have done that.

 

[AJ Bentley]

It looks like you picked up a wrong formula there. Take a look at 'Young's slits' in Wikipedia.