Light of frequency 5×10^4 is travelling in a medium of refractive index 1.5. What is the wavelength?

Question

Elena Albarran · Accepted Answer

#\lambda=\frac{c}{nf}=4000m#

To begin, let us define the refractive index:

#n=\frac{c}{v}#

#v=\lambda f#

Whence:

#n=\frac{c}{\lambda f}\implies \lambda=\frac{c}{nf}#

Now we can simply use the values we're given to calculate the wavelength (assuming that the speed of light is #300# million meters per second):

#\lambda=\frac{3\cdot 10^8}{5\cdot 10^4\cdot 1.5}=4000m#

HIX Tutor · Answer

undefined Great question! Let's find the wavelength together.

1. **What do we know about light?** 
   Light travels at different speeds in different materials.

2. **What is the formula for wavelength?** 
   Wavelength (λ) is related to frequency (f) and speed of light (c). The formula is:
   $$ λ = \frac{c}{f} $$

3. **What is the speed of light in the medium?**
   The speed of light in a vacuum (c) is about $3 × 10^8$ m/s. 
   In a medium, you can find the speed by dividing by the refractive index (n):
   $$ v = \frac{c}{n} $$
   Here, $n = 1.5$.

4. **Calculate the speed in the medium.**
   $$ v = \frac{3 × 10^8 \text{ m/s}}{1.5} = 2 × 10^8 \text{ m/s} $$

5. **Now, plug in the numbers into the wavelength formula.**
   You have the frequency $f = 5 × 10^4 \text{ Hz}$:
   $$ λ = \frac{v}{f} = \frac{2 × 10^8 \text{ m/s}}{5 × 10^4 \text{ Hz}} $$

6. **Calculate the wavelength.**
   $$ λ = 4000 \text{ m} $$

So, the wavelength is **4000 m**.

Does that make sense?