Question

Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is :

(1) \((2\sqrt2 +1) : (2\sqrt2 -1)\)

(2) \((3+ 2\sqrt2) : (3- 2\sqrt2)\)

(3) \(9 :1\)

(4) \(3 :1\)

Answer 1

Correct option is : (2) \((3+ 2\sqrt 2) : (3 - 2\sqrt2)\) 

\(I \propto \text{width}\)

\(I _{max} = \left(\sqrt I_1+ \sqrt I _2 \right)^2\)

\(\therefore \ I _1 = I_o, \ I_2 = 2I_0\)

\(I_{min} = \left(\sqrt I_1 - \sqrt {I_2}\right)^2\)

\(\frac{I_{max}}{I_{min}} = \frac{\left(\sqrt2+ 1\right)^2}{\left(\sqrt2 - 1\right)^2} \Rightarrow \frac{3 + 2 \sqrt2}{3-2 \sqrt2}\)