Question

An aperture of diameter 1.2 mm has been illuminated by monochromatic light. The diffracted light is observed on a screen. When the screen is gradually displaced towards the aperture, the centre becomes dark for the first time at a distance of 30cm from the aperture. The wavelength of light used is :

• A. 6000$A^o$
• B. 4000$A^o$
• C. 8000$A^o$
• D. 3000$A^o$

Answer 1

Answer: (A)

6000$A^o$

Given that diameter = $1.2mm=0.12cm$

Radius $r=0.06cm$

$b=30cm$

Here $(b^2+r^2)=(b+\lambda {)}^2$

${30}^2+(0.06{)}^2=(30+\lambda {)}^2$

$\lambda =\frac{(0.06{)}^{2}c{m}^2}{2\times 30cm}\left({\lambda }^{2}neglected\right)$

$=0.00006cm=6000\mathring{A}$