Question

In Young's double-slit experiment, the slits are $2mm$ apart and are illuminated with a mixture of two wavelengths ${\lambda }_0=750nm$ and $\lambda =900nm$. The minimum distance from the common central bright fringe on a screen $2m$ from the slits, where a bright fringe from one interference pattern coincides with a bright fringe from the other, is

• A. $1.5mm$
• B. $3mm$
• C. $4.5mm$
• D. $6mm$

Answer 1

The correct option is C $4.5mm$

For $\lambda =750nm$

$\beta =\lambda \frac{D}{d}=0.75mm$

Location of bright fringes = $0.75mm$ where n in natural number

Similarly

For $\lambda =900nm$

$\beta =\lambda \frac{D}{d}=0.90mm$

Location of bright fringes = $0.90mm$ where m in natural number

For both bright fringe to coincide $0.75n=0.9m$

This is satisfied first time for n = 6 and m = 5

Location of coinciding of bright fringes for first time = $6\ast 0.75=4.5mm$

Answer. C) 4.5 mm