In a single slit diffraction experiment first minimum for red light (660 nm) coincides with first maximum of some other wavelength ${\lambda }^{\mathrm{\prime }}.$ The value of ${\lambda }^{\mathrm{\prime }}$ is

In a single slit diffraction experiment, position of minima is given by d $\sin \theta =n\lambda$ 

so for first minima of red $\mathrm{sin\theta }=1\times \left(\frac{{\mathrm{\lambda }}_{\mathrm{R}}}{\mathrm{d}}\right)$ and as first maxima is midway between first and second minima, for wavelength ${\lambda }^{\mathrm{\prime }}\text{, }$ its position will be ${\mathrm{dsin\theta }}^{\mathrm{\prime }}=\frac{{\mathrm{\lambda }}^{\mathrm{\prime }}+2{\mathrm{\lambda }}^{\mathrm{\prime }}}{2}\Rightarrow {\mathrm{sin\theta }}^{\mathrm{\prime }}=\frac{3{\mathrm{\lambda }}^{\mathrm{\prime }}}{2\mathrm{d}}$ 

According to given condition $\sin \theta =\sin {\theta }^{\mathrm{\prime }}$ $\Rightarrow {\lambda }^{\mathrm{\prime }}=\frac{2}{3}{\lambda }_R$

$\text{ so }{\mathrm{\lambda }}^{\mathrm{\prime }}=\frac{2}{3}\times 6600=4400\text{Å}$