Question

If monochromatic light passes through a 0.050 mm slit and is projected onto a screen 0.70 m away with a distance of a 8.00 mm between the central bright band and the first dark band, what is the wavelength of the light?

Answer 1

The wavelength of the monochromatic light is approximately 540 nm.

Step-by-step explanation:

To find the wavelength of the monochromatic light, we can use the equation for calculating the slit width:

d*sin(θ) = m*λ

Where d is the slit width, θ is the angle between the central bright band and the first dark band, m is the order of the bright band, and λ is the wavelength of the light.

In this case, we need to rearrange the equation to solve for λ:

λ = d*sin(θ) / m

Substituting the given values, we have:

λ = (0.050 mm * sin(θ)) / 1

Since the distance between the central bright band and the first dark band is given as 8.00 mm, we can calculate the angle θ using the formula:

tan(θ) = opposite / adjacent = 8.00 mm / 0.70 m

θ = tan-1(8.00 mm / 0.70 m)

Using a scientific calculator, we find that θ is approximately 6.536°.

Substituting this angle back into the equation for λ, we can solve for the wavelength:

λ = (0.050 mm * sin(6.536°)) / 1

Calculating this expression, we find that the wavelength of the light is approximately 0.0054 mm or 540 nm.