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, $3^{\text {rd }}$ maximum of $\lambda_{2}$ overlaps with $5^{\text {th }}$ minimum of $\lambda_{1}$
• D. the angular separation of fringes of $\lambda_1$ is greater than $\lambda_2$

Answer 1

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

$\beta=\frac{ D \lambda}{ d }$
$\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)(600\, nm ) $
$=(2 \times 5-1)\left(\frac{ D }{2 d }\right) 400\, nm$
Angular width $\theta=\frac{\lambda}{ d }$