Question

A light source, which emits two wavelengths ${\lambda }_1=400$nm and ${\lambda }_2=600$nm, is used in a Young's double slit experiment. If recorded fringe widths for ${\lambda }_1$ and ${\lambda }_2$ are ${\beta }_1$ and ${\beta }_2$ and the number of fringes for them within a distance y on one side of the central maximum are m${}_1$ and m${}_2$, respectively, then

• A. ${\beta }_2>{\beta }_1$
• B. $m_1>m_2$
• C. From the central maximum, 3${}^{rd}$ maximum of ${\lambda }_2$ overlaps with 5${}^{th}$ minimum of ${\lambda }_1$
• D. The angular separation of fringes for ${\lambda }_1$ is greater than ${\lambda }_2$

Answer 1

Answer: (A), (B), (C)

The correct options are
A ${\beta }_2>{\beta }_1$
B $m_1>m_2$
C From the central maximum, 3${}^{rd}$ maximum of ${\lambda }_2$ overlaps with 5${}^{th}$ minimum of ${\lambda }_1$

$\beta =\frac{D\lambda }{d}$
$\because {\lambda }_2>{\lambda }_1\Rightarrow {\beta }_2>{\beta }_1$
Also $m_1{\beta }_1=m_2{\beta }_2\Rightarrow m_1>m_2$
Also $3\left(\frac{D}{d}\right)\left(600nm\right)=(2\times 5-1)\left(\frac{D}{2d}\right)400nm$
Angular width $\theta =\frac{\lambda }{d}$