a double slit located a distance x from a screen, with the distance from the center of the screen given by y. When the distance d between the slits is relatively large, there will be numerous bright spots, called fringes. It can be shown that, for small angles (where sin θ θ, with θ in radians), the distance between fringes is given by Δy = xλ/d. Using this result, find the wavelength of light that produces fringes 8.00 mm apart on a screen 2.00 m from double slits separated by 0.150 mm.

To find the wavelength of light that produces fringes 8.00 mm apart on a screen, we can use the formula Δy = xλ/d. We are given the values as follows:

Δy = 8.00 mm = 0.008 m (converting mm to meters)
x = 2.00 m
d = 0.150 mm = 0.00015 m (converting mm to meters)

So, the formula becomes:

0.008 m = 2.00 m * λ / 0.00015 m

To solve for λ (wavelength), we can rearrange the equation:

λ = (0.008 m * 0.00015 m) / 2.00 m

λ ≈ 6.00 × 10^-7 m

Therefore, the wavelength of light that produces fringes 8.00 mm apart on a screen is approximately 6.00 × 10^-7 meters (or 600 nm in nanometers).

To find the wavelength of light that produces fringes 8.00 mm apart on a screen 2.00 m from double slits separated by 0.150 mm, we can use the equation Δy = xλ/d.

Given:
Δy = 8.00 mm = 8.00 × 10^-3 m
x = 2.00 m
d = 0.150 mm = 0.150 × 10^-3 m

Plugging in the values, we have:
8.00 × 10^-3 m = (2.00 m)λ / (0.150 × 10^-3 m)

Now, let's solve for λ (wavelength).

Multiply both sides by (0.150 × 10^-3 m):
(8.00 × 10^-3 m) * (0.150 × 10^-3 m) = (2.00 m)λ

0.0012 m^2 = (2.00 m)λ

Divide both sides by 2.00 m:
0.0012 m^2 / 2.00 m = λ

λ = 0.0006 m = 600 nm

Therefore, the wavelength of light that produces fringes 8.00 mm apart on a screen 2.00 m from double slits separated by 0.150 mm is 600 nm.