Final answer:
The width of the narrow slit that produces a diffraction pattern can be calculated using the formula for single-slit diffraction.
Step-by-step explanation:
When light passes through a narrow slit, it undergoes diffraction, which leads to the formation of a diffraction pattern on a screen.
The width of the central peak of this pattern is determined by the width of the slit. In this case, the central peak is 1.0 m wide, and the screen is 1.8 m away from the slit.
We can use the formula for single-slit diffraction to calculate the width of the slit:
d = (λL) / w
Where d is the width of the central peak, λ is the wavelength of light, L is the distance from the slit to the screen, and w is the width of the slit. Plugging in the given values, we have:
w = (λL) / d
Calculating this value will give us the narrowness of the slit that produces the given diffraction pattern.