Question

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

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

Answer 1

The correct option is D $1.9$mm

Since in YDSE, angular width is given by

Angular Width $A.W.=\frac{\beta }{D}=\frac{\lambda }{d}$

For a given wavelength,

${A.W.}_1{d}_1={A.W.}_2{d}_2$

$0.20\times 2=0.21\times d_2$

$d_2=1.9mm$