Question
Explain the changes occuring in the wave length, speed and frequency when light enters from one mudium to the other medium.
✓
Answer
→As shown in the fig., a wavefront enters from a rarer to a denser medium.
→For medium (1), the wave length is $\lambda_1$, speed is $v_1$ and frequency $v_1$.
→Similary, for medium (2), the wavelength is $\lambda_2$, speed $v_2$ and frequency is $v_2$.
→Suppose, distance BC is equal to $\lambda_1$, so the distance AE will be equal to $\lambda_2$.
→Because if the crest from B has reached C , in time $\tau$, then the crest from A should have also reached E in time $\tau$.
→Thus, $\frac{ BC }{ AE }=\frac{\lambda_1}{\lambda_2}$
$\begin{aligned}
\quad BC & =v_1 \tau \\
AE & =v_2 \tau \\
\therefore \quad & \frac{v_1 \tau}{v_2 \tau}=\frac{\lambda_1}{\lambda_2} \\
\therefore \quad & \frac{\lambda_1}{\lambda_2}=\frac{v_1}{v_2}
\end{aligned}$
hence for $v_1>v_2$, so, $\lambda_1$ will be greater than $\lambda_2$.
$\text { (If } v_1>v_2, \lambda_1>\lambda_2 \text { ) }$
→The above equation implies that when a wave gets refracted into a denser medium, $\left(v_1>v_2\right)$, the wavelength and the speed of propogation decrease, but the frequency $\left(v=\frac{\nu}{\lambda}\right)$ remains the same.
→For medium (1), the wave length is $\lambda_1$, speed is $v_1$ and frequency $v_1$.
→Similary, for medium (2), the wavelength is $\lambda_2$, speed $v_2$ and frequency is $v_2$.
→Suppose, distance BC is equal to $\lambda_1$, so the distance AE will be equal to $\lambda_2$.
→Because if the crest from B has reached C , in time $\tau$, then the crest from A should have also reached E in time $\tau$.
→Thus, $\frac{ BC }{ AE }=\frac{\lambda_1}{\lambda_2}$
$\begin{aligned}
\quad BC & =v_1 \tau \\
AE & =v_2 \tau \\
\therefore \quad & \frac{v_1 \tau}{v_2 \tau}=\frac{\lambda_1}{\lambda_2} \\
\therefore \quad & \frac{\lambda_1}{\lambda_2}=\frac{v_1}{v_2}
\end{aligned}$
hence for $v_1>v_2$, so, $\lambda_1$ will be greater than $\lambda_2$.
$\text { (If } v_1>v_2, \lambda_1>\lambda_2 \text { ) }$
→The above equation implies that when a wave gets refracted into a denser medium, $\left(v_1>v_2\right)$, the wavelength and the speed of propogation decrease, but the frequency $\left(v=\frac{\nu}{\lambda}\right)$ remains the same.
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