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Chapter 16: Problem 2241

The frequency of a light wave in a material is \(4 \times 10^{14} \mathrm{~Hz}\) and wavelength is \(5000 \AA\). The refractive index of material will be take \(\left.\mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}\right)\) (A) \(1.5\) (B) \(1.7\) (C) \(1.33\) (D) None of these

Short Answer

Expert verified
The refractive index of the material is 1.5 (option A).

Step by step solution

01

Convert wavelength to meters

First, convert the wavelength from Angstroms to meters. 1 Angstrom (Å) is equal to \(1 \times 10^{-10}\) meters (m). So, the wavelength in meters is: \(λ = 5000 Å × \frac{1 \times 10^{-10} m}{1 Å} = 5 \times 10^{-7} m\)
02

Calculate the speed of light in the material

Now we can calculate the speed of light in the material (v) using the frequency (f) and wavelength (λ): v = f × λ v = \(4 \times 10^{14} Hz \ × \ 5 \times 10^{-7} m\) v = \(2 \times 10^{8}\) m/s
03

Find the refractive index

Finally, we can find the refractive index (n) using the speed of light in vacuum (c) and the speed of light in the material (v): n = c / v n = \(\frac{3 \times 10^{8} m/s}{2 \times 10^{8} m/s}\) n = 1.5 Therefore, the refractive index of the material is 1.5 which corresponds to option (A).

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Most popular questions from this chapter

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