Monochromatic light with a wavelength of 381 nm passes through a single slit and falls on a screen 85 cm away. If the distance of the first-order dark band is 0.43 cm from the center of the pattern, what is the width of the slit?

7.55 * 10^ (-5) m

Explanation:

Parameters given:

Wavelength of light, λ = 381 nm = 3.81 * 10^ (-7) m

Distance between screen and slit, L = 85 cm = 0.85 m

Distance of the first-order dark band from the center of the pattern, x = 0.43cm = 0.0043 m

The relationship between λ, L, x and the width of the slit, w is given as:

λ/w = x/L

=> w = λL/x

w = (3.81 * 10^ (-7) * 0.85) / (0.0043)

w = 7.55 * 10^ (-5) m