Question

A convex lens of diameter $8\text{cm}$ is used to focus to parallel beam of light of wavelength $6200\dot{\text{A}}$. If the light be focused at a distance of $20\text{cm}$ from the lens. What would be the radius of the central bright spot formed?

• A. $2.89\mu \text{m}$
• B. $1.5\mu \text{m}$
• C. $1.89\mu \text{m}$
• D. $1.79\mu \text{m}$

Answer 1

The correct option is C $1.89\mu \text{m}$


The angular spread of the central bright spot,

$\theta =\frac{1.22\lambda }{d}=\frac{1.22\times 6200\times {10}^{-10}}{8\times {10}^{-2}}$

$\therefore \theta =9.455\times {10}^{-6}$

As $\theta$ is small, from figure

$\theta =\frac{r}{D}$

$\Rightarrow r=\theta D=9.455\times {10}^{-6}\times 20\times {10}^{-2}\text{m}$

$=1.89\times {10}^{-6}\text{m}=1.89\mu \text{m}$

Hence, the correct option is $\left(C\right)$.

Note; The diffraction pattern due to circular aperture consists of a bright circular disc as a central maximum, which is called Airy's disc.