Given,

\(c=3\times {{10}^{8}}\) m/s is the speed of light.

\(3.75\times {{10}^{14}}\)Hz to \(7.5\times {{10}^{14}}\) Hz is the frequency range.

We know that,

Frequency x wavelength = light speed

If the frequency is \(3.75\times {{10}^{14}}\) ,

\(\lambda =\frac{c}{v}\)

\(\lambda =\frac{ 3\times {{10}^{8}} }{3.75\times {{10}^{14}} }\)

  \(\lambda =8\times {{10}^{-7}}\)

  \(\lambda =8000\overset{\circ }{\mathop{A}}\, \)

If the frequency is \(7.5\times {{10}^{14}}\) Hz

  \(\lambda =\frac{c}{v}\)

 \(\lambda =\frac{ 3\times {{10}^{8}} }{ 7.5\times {{10}^{14}} }\)

  \(\lambda = 4\times {{10}^{-7}}\) m

\(\lambda =4000\overset{\circ }{\mathop{A}}\,\)

Therefore, the answer is \(4000\overset{0}{\mathop{A}}\,\) to \(8000\overset{0}{\mathop{A}}\,\)