Question

White light consists of wavelengths from 400 nm to 700 nm. What will be the wavelength range seen when white light is passed through a glass of refractive index 1.55?

Answer 1

Let `lambda_1` and `lambda_2` be the wavelengths of light in water for 400 nm and 700 nm (wavelengths in a vacuum) respectively. Let `lambda_"a"` be the wavelength of light in vacuum.

`lambda_1 = lambda_"a"/"n" = (400 xx 10^-9 "m")/1.55 = 258.06 xx 10^-9  "m"`

`lambda_2 = lambda_"a"/"n" = (700 xx 10^-9 "m")/1.55 = 451.61 xx 10^-9` m

The wavelength range seen when white light is passed through the glass would be 258.06 nm to 451.61 run.

Answer 2

Given:

n = 1.55

Smallest wavelength = 400 nm,

Largest wavelength = 700 nm

To find: Range of wavelength of light when passed through the glass

Formula: `λ_"med" = λ_"vac"/"n"`

Calculation:

For the smallest wavelength (in glass),

From formula

`λ_"med" = 400/1.55`

= 2.5806 × 10² nm 

= 258.06 nm 

For largest wavelength

From formula,

`λ_"med" = 700/1.55`

= 4.5161 × 10² nm

= 451.61 nm

The wavelength range when white- light is passed through glass is 258.06 nm to 451.61 nm.