Light of certain color contain 2000 waves in the length of \(1 \mathrm{~mm}\) in air. What will be the wavelength of this light in medium of refractive index \(1.25\) ? (A) \(1000 \AA\) (B) \(2000 \AA\) (C) \(3000 \AA\) (D) \(4000 \AA\)

We are given that there are 2000 waves in 1 mm length in air. To find the wavelength per wave in air, we simply divide the total length (1 mm) by the number of waves (2000). Wavelength in air = Total length / Number of waves Wavelength in air = \( \frac{1\,mm}{2000} = 0.0005\,mm \) Remember that 1 nm = 1000 Å and 1mm = \(10^6 \,\mathrm{nm}\), so we can convert the wavelength in air to Ångströms: Wavelength in air = \( 0.0005\,mm \times \frac{10^6 \,\mathrm{nm}}{1 \mathrm{~mm}} \times \frac{1000 \,\mathrm{Å}}{1\,\mathrm{nm}} = 500 \, Å \) So, the wavelength of light in air is 500 Å.

Snell's law states that the product of the refractive index and the wavelength in the medium is equal to the product of the refractive index of air (which is 1) and the wavelength in air: \(n_{medium} \times \lambda_{medium} = n_{air} \times \lambda_{air} \) Since \(n_{air}\) = 1, \(n_{medium} \times \lambda_{medium} = \lambda_{air} \) We are given the refractive index of the medium which is 1.25. We can plug in the refractive index and the wavelength in air to find the wavelength in the medium. \( 1.25 \times \lambda_{medium} = 500\, Å \) To find the wavelength in the medium, divide both sides of the equation by the refractive index: \( \lambda_{medium} = \frac{500\,Å}{1.25} \) \( \lambda_{medium} = 400\,Å \) The wavelength of light in the medium is 400 Å, so the correct answer is (D) \(4000 \,Å\).