Question

The image of a star is formed by a convergent lens of focal length $1\text{m}$ and diameter $5\text{cm}.$ If the lens is ideal and the effective wavelength in image formation is taken as $5\times {10}^{-5}\text{cm},$ the diameter of the image formed will be nearest to

• A. Zero
• B. $2.5\times {10}^{-6}\text{cm}$
• C. $2.5\times {10}^{-5}\text{cm}$
• D. $2.5\times {10}^{-3}\text{cm}$

Answer 1

The correct option is D $2.5\times {10}^{-3}\text{cm}$

Radius of the central spot is given by,

$R=\frac{1.22\lambda f}{b}$

$\Rightarrow Dia=2R=2\times \frac{1.22\lambda f}{b}$

$\Rightarrow Dia=\frac{2\times 1.22\times (5\times {10}^{-5}\times {10}^{-2})\times \left(1\right)}{(5\times {10}^{-2})}$

$\Rightarrow Dia=2.5\times {10}^{-5}\text{m}$

$\therefore Dia=2.5\times {10}^{-3}\text{cm}$

Hence, option $\left(\text{D}\right)$ is correct.