TS EAMCET 5-Aug-2021 Shift 1 Question Paper

Given, wavelength of blue light in vacuum, $\lambda_{a}=450\,\mathrm{nm}=450 \times 10^{-9}\,\mathrm{m}$ Refractive index of medium, $\mu_{m}=1.5$ Speed of light in air or vacuum, $c=3 \times 10^{8}\,\mathrm{m}/\mathrm{s}$ $\lambda_{m}$ is the wavelength of light in medium. whereas $v_{m}$ is the speed of light in medium. As we know that, Refractive index of medium with respect to air, $\mu_{ma} \;\; = \frac{\mu_{m}}{\mu_{a}} = \frac{\lambda_{a}}{\lambda_{m}}$ $\therefore \;\; \lambda_{m} \;\; = \frac{\lambda_{a} \mu_{a}}{\mu_{m}}$ $\;\; = 450 \times 10^{-9} \times \frac{1}{1.5} = \frac{4500}{15} \times 10^{-9}$ $\;\; = 3 \times 10^{-7}\,\mathrm{m}$ $\text{ Since, } \;\; \frac{\mu_{m}}{\mu_{a}} = \frac{c}{v_{m}}$ $\Rightarrow \;\; v_{m} \;\; = c \frac{\mu_{a}}{\mu_{m}} = 3 \times 10^{8} \times \frac{1}{1.5}$ $= \;\; 2 \times 10^{8}\,\mathrm{ms}^{-1}$ Since, $\;\; f_{m} = \frac{v_{m}}{\lambda_{m}}$ where, $f_{m}$ is frequency of light in medium. $\therefore f_{m} \;\; = \frac{v_{m}}{\lambda_{m}}$ $\Rightarrow f_{m} \;\; = \frac{2 \times 10^{8}}{3 \times 10^{-7}} = 0.66 \times 10^{15}$ $\;\; = 6.67 \times 10^{14}\,\mathrm{Hz}$