Question

Calculate the wavelength of light used in an interference experiment from the following data: Fringe width $=0.03 \,cm$. Distance between slits and eyepiece through which the interference pattern is observed is $1 \,m$. Distance between the images of the virtual source when a convex lens of focal length $16 \,cm$ is used at a distance of $80\, cm$ from the eyepiece is $0.8\, cm$.

• A. $6000\,\mathring{A} $
• B. $0.00006\,\mathring{A} $
• C. $6000 \,cm$
• D. $0.00006 \,m$

Answer 1

Answer: (A)

$\beta=0.03\, cm , D=1\, m =100\, cm$
Distance between images of the source $=0.8\, cm$
Distance of image from lens, $v=80 \,cm$
Distance of slit from lens $=u$
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$ \Rightarrow \frac{1}{60}+\frac{1}{u}=\frac{1}{16} $
$\Rightarrow u=20 \,cm$
Magnification $=\frac{v}{u}=\frac{80}{20}=4$
Magnification $=\frac{\text { Distances between images of slits }}{\text { Distance between slits }}$
$=\frac{0.8}{d}=\frac{0.8}{d}=4$
$\Rightarrow d=0.2 \,cm$
$ \Rightarrow \beta=\frac{D \lambda}{d}=\frac{100 \lambda}{2}=0.03$
$\Rightarrow \lambda=6000\,\mathring{A} $