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Wave Optics — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsWave Optics3 Marks
Question

Consider a two slit interference arrangements such that the distance of the screen from the slits is half the distance between the slits.

Obtain the value of D in terms of $\lambda$ such that the first minima on the screen fall at a distance D from the centre O.
✓

Answer

$\text{T}_2\text{P}=\text{D}+\text{x},\text{T}_1\text{P}=\text{D}-\text{x}$ $\text{S}_1\text{P}=\sqrt{(\text{S}_1\text{T}_1)^2+(\text{P}\text{T}_1)^2}=[\text{D}^2+(\text{D}-\text{x}^2)]^\frac{1}{2}$ $\text{S}_2\text{P}=[\text{D}^2+\text{(D+x)}^2]^\frac{1}{2}$ Minima will occur when: $[\text{D}^2+(\text{D}+\text{x})^2]^\frac{1}{2}-[\text{D}^2+(\text{D}-\text{x})^2]^\frac{1}{2}=\frac{\lambda}{2}$ $\text{if}\text{ x}=\text{D},(\text{D}^2+4\text{D}^2)^\frac{1}{2}-\text{D}=\frac{\lambda}{2}$ $\Rightarrow \text{D}(\sqrt5-1)=\frac{\lambda}{2}\Rightarrow\text{D}=\frac{\lambda}{2(\sqrt5-1)}$

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