Question

Young's double-slit experiment is carried with two thin sheets of thickness $10.4\mu m$ 4ach 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 $400nm$ to $780nm$ is used, then which wavelength will form maxima exactly at point $O$, the centre of the screen?

• A. $416nm$ only
• B. $624nm$ only
• C. $416nm$ and $624nm$ only
• D. None of these

Answer 1

Answer: (C)

$416nm$ and $624nm$ only

For maxima at center path difference should be an integer multiple of $\lambda$
$({\mu }_1-1)t-({\mu }_2-1)t-\frac{yd}{D}=n\lambda$ given y=0
$({\mu }_1-{\mu }_2)t=n\lambda$
$.12\times 10.4\mu m=n\lambda$
$1248nm=n\lambda$
Checking option A $\lambda =416nm$

$\Rightarrow n=\frac{1248nm}{416nm}=3$ hence, it will have maxima at center
Checking option B $\lambda =624nm$

$\Rightarrow n=\frac{1248nm}{624nm}=2$ hence, it will have maxima at center
the correct answer is option C.