Question

Determine the difference $L_1-L_2(=\Delta L)$ in terms of ${\lambda }_0$.

• A. $\frac{4{\lambda }_0}{\mu }$
• B. $\frac{7{\lambda }_0}{2\mu }$
• C. $\frac{3{\lambda }_0}{\mu }$
• D. none of the above

Answer 1

The correct option is B $\frac{7{\lambda }_0}{2\mu }$

According to the question, at A and B dark fringe is formed.Thus there are 7 pairs of fringes ( bright + dark).

Hence, $\beta =\frac{L}{7}$

$\alpha =\frac{L_1-L_2}{L}$

$\beta =\frac{{\lambda }_o}{2\mu \alpha }$

Thus $\beta =\frac{{\lambda }_{o}L}{2\mu (L_1-L_2)}$

$⟹L_1-L_2=\frac{7{\lambda }_o}{2\mu }$