Physics - Wave Optics Question with Solution | TestHub

According to Rayleigh's criterion, the angular separation between two point sources just resolved by a telescope is given by $\Delta \theta =\frac{1.22\lambda }{D}$, where $\lambda$ is the wavelength of light and $D$ is the diameter of the objective lens.

The linear distance $x$ between the centres of their diffraction patterns in the focal plane of the lens is given by:

$x=f\Delta \theta =\frac{1.22\lambda f}{D}$

Given:
$D=5$ cm
$f=25$ cm
$\lambda =5000$ \AA

Substituting the given values:

$x=\frac{1.22\times 5000\text{ A˚}\times 25\text{ cm}}{5\text{ cm}}$

$x=1.22\times 5000\times 5$ \AA

$x=6.1\times 5000$ \AA

$x=30500$ \AA

Answer: $30500$ Å