Question

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

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

Answer 1

Answer: (A)

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