Question

In a YDSE, first minima for ${\lambda }_1=600\text{nm}$ coincides with the first maxima for wavelength ${\lambda }_2$. Calculate the value of ${\lambda }_2$.

• A. $600\text{nm}$
• B. $900\text{nm}$
• C. $1200\text{nm}$
• D. $300\text{nm}$

Answer 1

The correct option is D $300\text{nm}$

For minima :
$y=\left(\frac{2n-1}{2}\right)\frac{\lambda D}{d}$
From $n=1$
$y=\frac{\lambda D}{2d}$

For maxima,
$y=\frac{n\lambda D}{d}$
For $n=1$
$y=\frac{\lambda D}{d}$

According to the question :
$\frac{{\lambda }_{1}D}{2d}=\frac{{\lambda }_{2}D}{d}$
$\therefore {\lambda }_2=\frac{{\lambda }_1}{2}=\frac{600}{2}=300\text{nm}$