Question

To make the central fringe at the centre O, a mica sheet of refractive index 1.5 is introduced. Choose the correct statement –

• A. The thickness of sheet is $2\left( \sqrt{2} - 1 \right)$d in front of S₁
• B. The thickness of sheet is $2\left( \sqrt{2} - 1 \right)$d in front of S₂
• C. The thickness of sheet is $2\sqrt{2}$ d in front of S₁
• D. The thickness of sheet is $2\left( \sqrt{2} - 1 \right)$ d in front of S₁

Answer 1

Answer: (A)

The thickness of sheet is $2\left( \sqrt{2} - 1 \right)$d in front of S₁

Answer 2

Dx_{at O} = SS₂ + S₂O – [SS₁ + S₁O + (m _ 1)t]

= $\sqrt{2}$d – d – (m _ 1) t

0 = $\left( \sqrt{2} - 1 \right)$d – (1.5 – 1) t

$\frac{t}{2}$ = $\left( \sqrt{2} - 1 \right)$d

t = 2 $\left( \sqrt{2} - 1 \right)$d