Question

What is the wave length of light of frequency 5*10 14 Hz in the medium whose index of
refraction is 2.5 ? (c=3*10 8 m/s)

Answer 1

GIVEN:

• frequency (f)= 5×10^14 H z
• refractive index (n) = 2.5
• speed of light (c) =3×10^8

TO FIND :

• wavelength (w)

FORMULA:

• $n = \frac{v}{c} = \frac{fw}{c}$

As refractive index doesn't depend upon frequency

• $n = \frac{v}{c} = \frac{w}{c}$

SOLUTION:

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

$n = \frac{w}{c}$

$w = 2.5 \times 3 \times {10}^{8} \\ w = 7.5 \times {10}^{8}$

Answer 2

Answer:

400 nm  

Explanation:

Wavelength = velocity/frequency

Velocity = c/refractive index where c = 3x10^8 m/s is velocity of light in vaccum.

So,

Wavelegth = 3*10^8/(1.5*5.00*10^14)

= 3*10^8*2/(3*5*10^14)

= (2/5)* 10^(-6) m

= 0.4 micrometers or 400 nanometres