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प्रश्न
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?
उत्तर १
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.
उत्तर २
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.
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