Question

When the orange light passes from air ($n=1$) into glass ($n=1.5$), what is its new wavelength?

• A. $4\times {10}^{-7}m$
• B. $4\times {10}^{-6}m$
• C. $2.5\times {10}^{-7}m$
• D. $6\times {10}^{-7}m$
• E. $9\times {10}^{-7}m$

Answer 1

The correct option is A $4\times {10}^{-7}m$

When orange light passes through glass, the frequency will not change but velocity will be changed according to formula, $v=c/n$ where c be the velocity of light and n be the refractive index of the material. Also we know that $v=f\lambda$

Thus, $\frac{c}{n_a}=f{\lambda }_a....\left(1\right)$ and

$\frac{c}{n_g}=f{\lambda }_g....\left(2\right)$

using (1), (2) becomes, $\frac{n_{a}f{\lambda }_a}{n_g}=f{\lambda }_g$

So, ${\lambda }_g=\frac{n_a}{n_g}{\lambda }_a=\frac{1}{1.5}\times 600\times {10}^{-9}=4\times {10}^{7}m$ (as wavelength of orange light in air is $600nm$)