Question

Two pinholes $1.5\text{mm}$ apart are placed in front of a source of light of wavelength $5.5\times {10}^{-5}\text{cm}$ and seen through a telescope with its objectives stopped down to a diameter of $0.4\text{cm}.$ Find the maximum distance from the telescope at which the pinholes can be resolved.

• A. $20\text{m}$
• B. $9\text{m}$
• C. $4\text{m}$
• D. $7\text{m}$

Answer 1

The correct option is B $9\text{m}$

Given, $\lambda =5.5\times {10}^{-5}\text{cm};D=0.4\text{cm}x=1.55\text{mm}=0.15\text{cm}$

As we know, resolving power of a telesope,

$\frac{1}{d\theta }=\frac{1.22\lambda }{D}$

Where, $d\theta =\text{Angular separation between two distant objects}D=\text{Diameter of the telescope's objective lens}$

$d\theta =\frac{1.22\lambda }{D}$

Also $d\theta =\frac{x}{d}$

$\therefore \frac{x}{d}=\frac{1.22\lambda }{D}$

$d=\frac{xD}{1.22\lambda }$

$d=\frac{0.15\times 0.4}{1.22\times 5.5\times {10}^{-5}}$

$d=894.2\text{cm}=8.942m\approx 9\text{m}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.