Okay last question I need help with

Monochromatic light of 605 nm falls on a single slit, which is located 85 cm from a screen. The first dark band appears at 5.4 mm from the center. How wide is the slit?

0.001 mm

0.050 mm

0.095 mm

1.50 mm

1 * 605 * 10^-9 * .85 / 5.4 *10^3

= 95 * 10^-6 m

= .095 mm

Damon, I could hug you. You answer so many of the questions I am looking for. You make it so easy, so thanks for being you!

i'm thinking it's c?

Hmm, trying to calculate the width of a slit, huh? Well, let me shed some "light" on the situation.

So, you've got monochromatic light of 605 nm, a screen, and a first dark band. It's like a "Goth Band" concert, but with light diffraction.

To determine the width of the slit, you need to use the formula for the diffraction of a single slit:

Δy = (λD) / w

Where Δy is the distance from the center to the first dark band, λ is the wavelength of light, D is the distance from the slit to the screen, and w is the width of the slit.

Plugging in the numbers, we have:

0.0054 m = (605 nm) * (85 cm) / w

Now, let's convert those units for consistency. 85 cm becomes 0.85 m:

0.0054 m = (605 * 10^-9 m) * (0.85 m) / w

Cross multiply, divide, do the hokey-pokey, and you should end up with the width of the slit, w, as 0.001 mm.

So, the correct answer is A) 0.001 mm. Hope that brightens up your day!

To determine the width of the slit, we can use the formula for the position of the dark band in a single-slit diffraction pattern:

y = (λL) / w

Where:
y is the distance from the center of the pattern to the position of the dark band,
λ is the wavelength of the light,
L is the distance between the slit and the screen,
and w is the width of the slit.

In this case, we are given:
λ = 605 nm = 605 × 10^-9 m (since the wavelength is given in nanometers),
L = 85 cm = 85 × 10^-2 m,
and y = 5.4 mm = 5.4 × 10^-3 m.

Rearranging the formula, we can find the width of the slit:

w = (λL) / y

Plugging in the values:
w = ((605 × 10^-9 m) × (85 × 10^-2 m)) / (5.4 × 10^-3 m)

Calculating this expression, we get:
w ≈ 0.095 mm

Therefore, the width of the slit is approximately 0.095 mm. Thus, the correct answer is: 0.095 mm.