Question

In a Young's double slit experiment, a laser light of $560\text{nm}$ produces an interference pattern with consecutive bright fringes' separation of $7.2\text{mm}$. Now, another light is used to produce an interference pattern with consecutive bright fringes' separation of $8.1\text{mm}$. The wavelength of second light is $\text{nm}$.

Answer 1

Given:
Wavelength of laser light:
$\lambda =560\times {10}^{-9}\text{nm}$
Fringes' separation:
${\beta }_1=7.2\times {10}^{-3}\text{mm}$
${\beta }_2=8.1\times {10}^{-3}\text{mm}$
As we know that, fringe separation is directly proportional to wavelength of light so:

$\frac{{\beta }_1}{{\beta }_2}=\frac{{\lambda }_1}{{\lambda }_2}$

$\Rightarrow {\lambda }_2=\frac{560\times {10}^{-9}\times 8.1\times {10}^{-3}}{7.2\times {10}^{-3}}$

$=6.3\times {10}^{-7}\text{m}=630\text{nm}$