In a YDSE experiment, the two slits are covered with a transparent membrane of negligible thickness which allows light to pass through it but does not allow water. A glass slab of thickness t $$=$$ $$0.41$$ mm and refractive index μ$$g=1.5$$ is placed in front of one of the slits as shown in the figure. The separation between the slits is d $$=$$ $$0.30$$ mm. The entire space to the left of the slits is filled with water of refractive index μ$$w=4/3$$ .A coherent light of intensity I and absolute wavelength λ$$=5000Ao$$ is being incident on the slits making an angle $$30$$º with horizontal. If screen is placed at a distance D $$=1m$$ from the slits, then the distance of central maxima from O is n×$$0.83$$ cm. Then the value of n is

Question

In a YDSE experiment, the two slits are covered with a transparent membrane of negligible thickness which allows light to pass through it but does not allow water. A glass slab of thickness t $$=$$ $$0.41$$ mm and refractive index μ$$g=1.5$$ is placed in front of one of the slits as shown in the figure. The separation between the slits is d $$=$$ $$0.30$$ mm. The entire space to the left of the slits is filled with water of refractive index μ$$w=4/3$$ .A coherent light of intensity I and absolute wavelength λ$$=5000Ao$$ is being incident on the slits making an angle $$30$$º with horizontal. If screen is placed at a distance D $$=1m$$ from the slits, then the distance of central maxima from O is n×$$0.83$$ cm. Then the value of n is

Infinity Learn · Accepted Answer

If central maxima is formed at point P on the screen, then the path difference due to water medium is cancelled by path difference due to glass slab.  For central bright spot, Δ$$x=0$$⇒$$S2P+$$μg−$$1t$$−$$S1P+$$μwdsin⁡$$30$$∘$$=0$$⇒$$S2P$$−$$S1P=xdD=$$μwdsin⁡$$300$$−μg−$$1$$×t⇒$$x=$$−$$1.66cm$$

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