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The wavelength of yellow sodium light in air is 589 nm. (a) What is its frequency? (b) What is its wavelength in glass whose index of refraction is 1.52? (c) From the results of (a) and (b), find its speed in this glass.

Short Answer

Expert verified
  1. The frequency of yellow sodium light is 5.09×1014Hz.
  2. The wavelength of the light when traveling through the glass is 388nm
  3. The light speed when traveling through the glass is1.97×108m/s

Step by step solution

01

Given information

The wavelength of yellow sodium light in air is λ=589nm.

The index of refraction of glass is,n=1.52.

02

Frequency of a wave

The frequency of a wave can be calculated mathematically by dividing the value of the wavelength from the speed of light.

So, if the wavelength increases then the value of frequency of the wave decreases accordingly.

03

(a) Frequency of yellow sodium light

The formula for the frequency of yellow sodium light is given by,

f=cλ

Here, speed of lightc=3×108m/s

Putting the values,

f=3×108m/s589×10-9mf=5.09×1014Hz

Hence, the frequency of yellow sodium light is5.09×1014Hz

04

(b) Wavelength when traveling through the glass

The formula for the wavelength of the light when traveling through the glass is given by,

λn=λnλn=589nm1.52λn=387.5nm

Hence, the wavelength of the light when traveling through the glass is387.5nm

05

(c) Light speed when traveling through the glass

The formula for the light speed when traveling through the glass is given by,

v=fλn

Putting values of f and λn,

v=5.09×1014Hz×387.5×10-9mv=1.97×108m/s

Hence, the light speed when traveling through the glass is1.97×108m/s

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