Question

In Young's double slit experiment the separation $d$ between the slits is $2mm$. The wavelength $\lambda$ of the light used is $5896\AA$ and distance $D$ between the screen and slits is $100cm$. It is found that the angular width of the fringes is $0.20°$. To increase the fringe angular width to $0.21°$ (with same $\lambda$ and $D$) the separation between the slits needs to be changed to

• A. $1.8mm$
• B. $1.9mm$
• C. $2.1mm$
• D. $1.7mm$

Answer 1

The correct option is B $1.9mm$

$\theta =\frac{\lambda }{d},\frac{{\theta }_1}{{\theta }_2}=\frac{d_2}{d_1}\frac{0.20}{0.21}=\frac{d_2}{2}\Rightarrow d_2=\frac{0.20}{0.21}\times 2=1.9mm$