An electromagnetic wave of frequency $3\times {10}^{6}Hz\left(3.0MHz\right)$ passes from vacuum into a non magnetic medium with permittivity,  $\in =16{\in }_0$, where ${\in }_0$ is the free space permittivity. The change in wavelength is

when an electro magnetic wave travels from one medium to another medium its frequency remains constant but its velocity and wavelength will change.Speed of electronmagnetic wave in vacuum is  $C=\frac{1}{\sqrt{{\mu }_0{\in }_0}}=f\lambda$
Where $\text{'}f\text{'}$ is frequency and $\text{'}\lambda \text{'}$ is wavelength of electromagnetic wave.
Speed of electromagnetic wave in a medium is $C\text{'}=\frac{1}{\sqrt{k{\mu }_0{\in }_0}}$ where ‘K’ is dielectric constant
$C\text{'}=f\lambda \text{'}$ where $\lambda \text{'}$ is wave length of electromagnetic wave in medium
$$\begin{gathered} Dividing the two speeds we get \\ \frac{f\lambda \text{'}}{f\lambda }=\frac{1}{\sqrt{k}} \\ \Rightarrow \lambda \text{'}=\frac{\lambda }{\sqrt{k}} \\ \Rightarrow \lambda \text{'}=\frac{\lambda }{\sqrt{\frac{\in }{{\in }_0}}} \left(\therefore k=\frac{\in }{{\in }_0}\right) \end{gathered}$$     
$\Rightarrow \lambda \text{'}=\frac{\lambda }{\sqrt{16}}=\frac{\lambda }{4}$  

Change in wavelength is  $\lambda \text{'}-\lambda$
$\Rightarrow \lambda \text{'}-\lambda =\frac{\lambda }{4}-\lambda =-\frac{3}{4}\lambda =-\frac{3}{4}\frac{c}{f} \left(\therefore \lambda =\frac{{\displaystyle c}}{{\displaystyle f}}\right)$   
$\Rightarrow \lambda \text{'}-\lambda =-\frac{3}{4}\times \frac{3\times {10}^8}{3\times {10}^6}=-\frac{3}{4}\times {10}^2$ 
$\Rightarrow \lambda \text{'}-\lambda =-75m$