The central maximum in the single-slit diffraction pattern can be calculated using the formula:
```
λ / w
```
Here, `λ` represents the wavelength of light and `w` represents the width of the slit.
First, we need to convert the provided values of `λ` and `w` into consistent units. The wavelength λ = 750 nm needs to be converted to meters. Knowing that 1 nm = 1e-9 m, we can do this by multiplying:
750 nm * 1e-9 = 750 * 10^-9 m.
Likewise, the slit width w is given as 1.0 x 10^⁻³ mm. To convert this to meters, we use the conversion factor 1 mm = 1e-3 m, leading to:
1.0 * 10^-3 mm * 1e-3 = 1.0 * 10^-3 * 10^-3 m.
Substituting λ = 750 * 10^-9 m and w = 1.0 * 10^-3 * 10^-3 m into the formula, we find the angular width of the central maximum in radians:
λ / w = (750 * 10^-9 m) / (1.0 * 10^-3 * 10^-3 m) = 0.75 radians.
Next, we convert the angular width from radians to degrees. The conversion factor is 180 degrees/π radians, so we multiply:
0.75 radians * (180/π) = 42.97 degrees.
So, the angular width of the central maximum caused by diffraction of 750 nm light through a 1.0 x 10⁻³mm-wide slit is approximately 0.75 radians, which is equivalent to approximately 42.97 degrees.