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.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
An electric field $\vec{\text{E}}=(\vec{\text{i}}20+\vec{\text{j}}30)\text{N}\text{C}^{-1}$ exists in the space. If the potential at the origin is taken to be zero, find the potential at (2m, 2m).
→A particle is moving 1.5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is $1.813 \times 10^{-4}$. Calculate the particle's mass and identify the particle.
→An iron needle is attracted to the ends of a bar magnet but not to the middle region of the magnet. Is the material making up the ends of a bar magnet different from that of the middle region?
State Bohr’s quantisation condition of angular momentum. Calculate the shortest wavelength of the Bracket series and state to which part of the electromagnetic spectrum does it belong.
A convex lens of focal length 25 cm is placed coaxially in contact with a concave lens of focal length 20 cm. Determine the power of the combination. Will the system be converging or diverging in nature?
Do all the electrons that absorb a photon come out as photoelectrons?
Give the characteristics of an electric field.
Explain the arrangment of Geiger-Marsden's experiment of $\alpha$-particle scattering.
→Explain current formed in solid conductors in presence of external electric field.
State types of commercial generators.