Question

A double slit interference experiment is conducted with light waves of wavelength of $650\text{nm}$ passing through two $3.0\mu m$ slits that are $18\text{m}$ apart. If the light wavelength is changed to $450\text{nm}$, then what can be commented regarding the width of the central maxima and the number of bright interference fringes it encloses?

• A. Increases
• B. Decreases
• C. Remains Same
• D. Becomes zero

Answer 1

The correct option is C Remains Same

First order minima expression:
$a\sin \theta =\lambda$
$\frac{ay}{D}=\lambda$
$y=\frac{\lambda D}{a}$
If we put this same value of $y$ in optical path difference of maxima,
$\Rightarrow \frac{yd}{D}$
$=\frac{\lambda D}{a}\times \frac{d}{D}$
$=\frac{d}{a}\lambda$

If we observe with change in $\lambda$ the width would change but the order or no.of fringes i.e., $\frac{d}{a}$ is not changing. So, no of fringes wont change.