Question

In Young's experiment a beam of light of wavelength $6500\mathring{A}$ and $5200\mathring{A}$ is used. Find the minimum distance from the central bright frings where bright frings produced by both the wavelength get superposed. The distance between two slits is $0.5mm$ and the distance between the slits and the screen is $100cm$.

Answer 1

If $n$ least no of fringed of ${\lambda }_e=6500A^o$

which are coincident with $(n+1)$ of $d_2=5200A^{-}$

$y^{\prime }=\eta \beta =(\eta +1){\beta }^{\prime }$

ie $\frac{\eta +1}{n}=\frac{\beta }{{\beta }^{\prime }}=\frac{{\lambda }_1}{{\lambda }_2}$

of

$\eta =\frac{{\lambda }_2}{{\lambda }_1-{\lambda }_2}=\frac{5200}{6500-5200}$

$=\frac{5200}{1300}$

$=4$

also $\beta =\frac{\lambda D}{d}$

substituting values of $\lambda ,D$

$\beta =0.13cm$

So $y^{\prime }=\eta \beta =4\times 0.13$

$=0.52cm$

$y^{\prime }=0.52cm$