Question

In a single slit diffraction experiment, first minimum of red light $\left(660 nm\right)$ coincides with the first maximum of some other wavelength $\lambda $ . The value of $\lambda $ in $nm$ is:

Answer 1

The angular position of first minimum for red light of wavelength $\lambda _{r}$ is given by $sin\theta _{1}=\frac{\lambda _{r}}{a}$
The angular position of first maximum for light of wavelength $\lambda ^{'}$ is given by $sin\theta _{1}^{'}=\frac{3 \lambda ^{'}}{2 a}$
According to given condition, $sin\theta _{1}=sin\theta _{1}^{'}$
$\Rightarrow \frac{\lambda _{r}}{a}=\frac{3 \lambda ^{'}}{2 a}$
$\Rightarrow \lambda ^{'}=\frac{2 \lambda _{r}}{3}$
$=\frac{2}{3}\times 660$
$=440nm$