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

Solution

## The correct option is B $$416nm$$ and $$624nm$$ onlyFor maxima at center path difference should be an integer multiple of $$\lambda$$$$(\mu_1-1)t-(\mu_2-1)t- \dfrac{yd}{D}= n\lambda$$ given y=0$$(\mu_1-\mu_2)t= n\lambda$$ $$.12\times 10.4 \mu m=n\lambda$$ $$1248\; nm =n\lambda$$  Checking option A $$\lambda=416 nm$$  $$\Rightarrow n=\dfrac{1248 nm}{416 nm}=3$$ hence, it will have maxima at centerChecking option B $$\lambda=624 nm$$ $$\Rightarrow n=\dfrac{1248 nm}{624nm}=2$$ hence, it will have maxima at centerthe correct answer is option C.PhysicsNCERTStandard XII

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