Question

When a thin wedge-shaped film is illuminated by a parallel beam of light of wavelength 6000 A${}^{\circ }$, 7 fringes are observed in a certain region of the film. What will be the number of fringes observed in the same region of a film if light of wavelength 4200 A${}^{\circ }$ is used?

• A. $6$
• B. $10$
  
• C. $14$
• D. $18$

Answer 1

The correct option is B $10$

In thin wedge - shaped film
$2\mu d=n\lambda$
where, $\mu$ is refractive index of the film
$d$ is separation between two surfaces
$n$ is number of fringes
$\lambda$ is wavelength of light
So, here in the problem we are changing the wavelength of the light keeping $\mu$ and $d$ same
So, n will change such that $n\lambda$ will remain same.
so, $n_1{\lambda }_1=n_2{\lambda }_2$
$7\times 6000=n_2\times 4200$
$\Rightarrow n_2=10$