Question

Young's double-slit experiment is carried with two thin sheets of thickness $10.4\mu m$ each and refractive index ${\mu }_1=1.52$ and ${\mu }_2=1.40$ covering the slits $S_1$ and $S_2$ respectively. If white light of range $400\text{nm}$ to $780\text{nm}$ is used, then which wavelength will form maxima at point $O$, the center of the screen?

• A. $416\text{nm}$ only
• B. $624\text{nm}$ only
• C. $416\text{nm}$ and $624\text{nm}$ only
• D. None of these

Answer 1

The correct option is C $416\text{nm}$ and $624\text{nm}$ only

Path difference at $O$$=({\mu }_2-{\mu }_1)t=12480\AA$
For maxima,
$n\lambda =12480\AA$
${\lambda }_1=12480\AA$
${\lambda }_2=6240\AA$
${\lambda }_3=4160\AA$
${\lambda }_4=3120\AA$
Therefore, only $6240\AA$ and $4160\AA$ exist in the spectrum.