Question

A broad source of light (l = 680 nm) illuminates normally two glass plates 120 mm long that touch at end and are separated by a wire 0.048 mm in diameter at the other end. The total number of bright fringes that appear over the 120 mm distance is:

• A. 50
• B. 100
• C. 141
• D. 400

Answer 1

The correct option is C 141

Fringe Width $\beta$ in case of variable thickness wedge shaped film is ;

$\beta =\frac{\lambda }{2\mu \theta }$

we get $\mathrm{Tan}\theta =\theta =\frac{y}{I}............\left(1\right)$

Let $N$ be the number of gringes formed over length $I$

$\begin{array}{c}I=N\beta \\ I=N\left(\frac{\lambda }{2\mu \theta }\right)\\ N=\frac{2\mu \theta }{\lambda }\\ N=\frac{2uY}{\lambda }\left[\because \theta =\frac{y}{I}\right]\\ N=\frac{2\times 1\times 0.048\times {10}^{-2}}{680\times {10}^9}\\ N=\frac{0.096\times {10}^{-2}}{680\times {10}^9}\\ N=141\end{array}$