Question

When a light wave of frequency $5\times {10}^{14}$ Hz is passed through a medium of refractive index 1.5 then its wavelength will become

• A. 4000$\mathring{A}$
• B. 4500$\mathring{A}$
• C. 6000$\mathring{A}$
• D. 9000$\mathring{A}$

Answer 1

Answer: (A)

4000$\mathring{A}$

Answer is A.
The frequency of the light doesn't actually change when the light crosses a boundary, only the wavelength does. Thus $n=c/v=c/(f\lambda$) and is thus inversely proportional to the wavelength.
In this case, refractive index $n=1.5$ and frequency $f=5\times {10}^{14}Hz$.
Velocity of light is $3\times {10}^{8}m/s$.
Substituting these values in $n=c/\left(f\lambda \right)$, we get,
$1.5=3\times {10}^{8}m/s$ / ($5\times {10}^{14}Hz$ $\times$ $\lambda$).
Therefore, $\lambda =0.4\times {10}^6=4000\mathring{A}$.
Hence, the wavelength will become $4000\mathring{A}$.