Please I need help with this physics problem. I would like to see the steps on how to solve it. Thank you!!!

Question

Th frequency of a light wave is 2.3x10^14 Hz. what is the wavelength, in nm, of this wave when it enter glass with an index of refraction of 1.6?

Answer 1

Let

f = 2.3×10¹⁴ Hz be the light's frequency,

λ (to be computed) be the light's wavelength in glass,

v (unknown) be the light's speed in glass,

c = 3×10⁸ m/s be light's speed in vacuum,

n = 1.6 be the index of refraction of glass.

You need to know two relations:

1) v = λf

This comes from considering properties of waves in general.

2) n = c/v

This is the definition of index of refraction n.

Combining the two,

λ = v/f = c/nf

Substituting actual numbers

λ = 3×10⁸/(1.6×2.3×10¹⁴) = 0.815×10^-6 m = 815 nm

By the way, this is not visible light, it is infrared.