Light of wavelength 560 nm passes through a pinhole of diameter...

The angular radius of the central bright spot (Airy disk) formed by diffraction through a circular aperture (pinhole) is given by:

$\theta = \dfrac{1.22 \lambda}{d}$

where $\lambda$ is the wavelength of light and $d$ is the diameter of the pinhole.

The linear radius of the central bright spot on a screen at a distance $D$ is:

$R = D\theta = \dfrac{1.22 \lambda D}{d}$

The diameter of the central bright spot is:

$D_{\text{spot}} = 2R = \dfrac{2.44 \lambda D}{d}$

Given values:
$\lambda = 560 \text{ nm} = 560 \times 10^{-9} \text{ m}$
$d = 0.20 \text{ mm} = 0.20 \times 10^{-3} \text{ m}$
$D = 2.00 \text{ m}$

Substituting the values into the formula:

$D_{\text{spot}} = \dfrac{2.44 \times 560 \times 10^{-9} \times 2.00}{0.20 \times 10^{-3}}$

$D_{\text{spot}} = 2.44 \times 560 \times 10^{-6} \times 10$

$D_{\text{spot}} = 2.44 \times 5.6 \times 10^{-3} \text{ m}$

$D_{\text{spot}} = 13.664 \times 10^{-3} \text{ m} = 1.3664 \text{ cm}$

Rounding to two decimal places, we get $1.37 \text{ cm}$.