Search any question & find its solution
Question:
Answered & Verified by Expert
If frequency $(v)$ of light is $5 \times 10^{16} \mathrm{~Hz}$ and speed of light in air is $3 \times 10^8 \mathrm{~m} / \mathrm{s}$. Find the ratio of wavelength of light in a medium of refractive index ' 2 ' to air
Options:
Solution:
2731 Upvotes
Verified Answer
The correct answer is:
2
$\mathrm{v}=v \lambda$, Here, $v$ is same as source of light.
$\begin{aligned}
& \Rightarrow \quad \mathrm{v} \propto \lambda, \frac{v_1}{v_2}=\frac{\lambda_1}{\lambda_2} \\
& \text { But } \mathrm{v}_1=\frac{\mathrm{c}}{\mathrm{n}_1}, \mathrm{v}_2 \text { (in air) }=\frac{\mathrm{c}}{\mathrm{n}_2}=\mathrm{c} \\
& \Rightarrow \quad \frac{\lambda_1}{\lambda_2}=\frac{\mathrm{c} / \mathrm{n}_1}{\mathrm{c}}=\frac{1}{\mathrm{n}_1}=\frac{1}{2} \Rightarrow \mathrm{n}_1=2
\end{aligned}$
$\begin{aligned}
& \Rightarrow \quad \mathrm{v} \propto \lambda, \frac{v_1}{v_2}=\frac{\lambda_1}{\lambda_2} \\
& \text { But } \mathrm{v}_1=\frac{\mathrm{c}}{\mathrm{n}_1}, \mathrm{v}_2 \text { (in air) }=\frac{\mathrm{c}}{\mathrm{n}_2}=\mathrm{c} \\
& \Rightarrow \quad \frac{\lambda_1}{\lambda_2}=\frac{\mathrm{c} / \mathrm{n}_1}{\mathrm{c}}=\frac{1}{\mathrm{n}_1}=\frac{1}{2} \Rightarrow \mathrm{n}_1=2
\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.