Question

A beam of monochromatic blue light of wavelength $4200\mathring{A}$ in air, travels in water of refractive index $\frac{4}{3}$. What is its wavelength in water?

• A. $4200\mathring{A}$
• B. $5600\mathring{A}$
• C. $3150\mathring{A}$
• D. $3850\mathring{A}$

Answer 1

Answer: (C)

$3150\mathring{A}$

The wavelength of the light rays is inversely proportional to the refractive index of the medium through which the beam is passing.

$\therefore \lambda \propto \frac{1}{\mu }$

Therefore, we can write-

$\frac{{\lambda }_{air}}{{\lambda }_{water}}=\frac{{\mu }_{water}}{{\mu }_{air}}$

${\lambda }_{water}={\lambda }_{air}.\frac{{\mu }_{air}}{{\mu }_{water}}$

${\lambda }_{water}=\left(4200A^{\circ }\right)\times \frac{1}{\left(\frac{4}{3}\right)}$

${\lambda }_{water}=3150A^{\circ }$

So, option (C) is correct.