Question

in glass, light travels with a speed of 2.0×10^8 m/s. light with a frequency of 3.1×10^14 hz moves through the glass. what is the wavelength of the light?

a. 1.6×10^(-23) m
b. 6.5×10^(-7) m
c. 1.6×10^6 m
d. 6.2×10^22 m

Explanation:

Step1: Recall the wave - speed formula

The wave - speed formula is $v = f\lambda$, where $v$ is the speed of the wave, $f$ is the frequency, and $\lambda$ is the wavelength. We need to solve for $\lambda$, so we can rewrite the formula as $\lambda=\frac{v}{f}$.

Step2: Substitute the given values

We are given that $v = 2.0\times10^{8}\ m/s$ and $f = 3.1\times10^{14}\ Hz$. Substituting these values into the formula $\lambda=\frac{v}{f}$, we get $\lambda=\frac{2.0\times 10^{8}\ m/s}{3.1\times 10^{14}\ Hz}$.

Step3: Perform the calculation

Using the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $\lambda=\frac{2.0}{3.1}\times10^{8 - 14}\ m$. $\frac{2.0}{3.1}\approx0.65$, and $10^{8 - 14}=10^{-6}$. So $\lambda\approx0.65\times10^{-6}\ m = 6.5\times10^{-7}\ m$.

Answer:

B. $6.5\times 10^{-7}\ m$