Question

In Y.D.S.E. the fringe width is 0.2 mm. If
wavelength of light is increase by 10% and
separation between the slits is increased by 10%
then fringe width will be:
1) 0.20 mm
(2) 0.165 mm
3) 0.401 mm
(4)0.242 mm
​

Answer 1

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Answer 2

Given :

Fringe width , $\beta=0.2 \ mm$ .

To Find :

New fringe width .

Solution :

We know , fringe width id given by :

$\beta=\dfrac{\lambda D}{d}$

Let , new wavelength be ,

$\lambda'=\lambda+\dfrac{10\lambda}{100}\\\\\lambda'=\dfrac{110\lambda}{100}$

Also , new separation between the slits is :

$d'=d+\dfrac{10d}{100}\\\\d'=\dfrac{110d}{100}$

Therefore , new fringe width is given by :

$\beta'=\dfrac{\lambda'D}{d'}\\\beta'=\dfrac{\dfrac{110}{100}\lambda D}{\dfrac{110}{100}d}\\\\\beta'=\dfrac{\lambda D}{d}=\beta$

Therefore , new fringe width will be same as initial fringe width .

Learn More :

Y.D.S.E

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