In a Young's double slit experiment, a combination of two glass wedges A and B , having refractive indices 1.7 and 1.5, respectively, are placed in front of the slits, as shown in the figure. The

Question

In a Young's double slit experiment, a combination of two glass wedges $A$ and $B$ , having refractive indices 1.7 and 1.5, respectively, are placed in front of the slits, as shown in the figure. The separation between the slits is $d = 2 mm$ and the shortest distance between the slits and the screen is $D = 2 m$ . Thickness of the combination of the wedges is $t = 12 μ m$ . The value of $l$ as shown in the figure is 1 mm . Neglect any refraction effect at the slanted interface of the wedges. Due to the combination of the wedges, the central maximum shifts (in mm ) with respect to O by ______

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TestHub · Accepted Answer

​ x + y = 12 μ m 12 4 ​ = x 1 ​ x = 3 μ m y = 6 μ m ​ ​ ∴ Δ = D y d ​ − ( μ B ​ − 1 ) x − ( μ A ​ − 1 ) y + ( μ B ​ − 1 ) y + ( μ A ​ − 1 ) x D − y d ​ = − 0.5 × 3 − 0.7 × 9 + 0.5 × 9 + 0.7 × 3 D − y d ​ = − 0.5 × 6 − 0.7 × 6 ⇒ D − y d ​ = − 1.2 μ m ⇒ y = d 1.2 × D ​ = 2 × 1 0 − 3 1.2 × 2 ​ × 1 0 − 6 = 1.2 mm ​

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