Question

Find the speed of light of wavelength lambda =780nm (in air) in a medium of refractive index mu=1.55. (b) What is the wavelength of this light in the given medium ?

Answer 1

Answer:

780/1.55nm

Explanation:

hope the answer will help you

Answer 2

Given that,

Refractive index of medium $( \mu_m) = 1.55$

Wavelength of light $(\lambda_l) = 780nm$

Speed of light when in vacuum $(c) = 3\times 10^8 m/s$

Refractive index of air =  $\mu_a$

(A)

        We have to find out the speed of light in a medium

        The refractive index formula is given by

                                  $\mu = \frac{c}{v}$

Here

            $\mu$ = refractive index of the medium

            $c$ = speed of light when in vacuum

            $v$ = speed of light when in medium

So,

               $v = \frac{c}{\mu_m} \\ = \frac{3\times10^8}{1.55} \\ = 1.94 \times 10^8 m/s$

Thus,  Speed of light when in medium $= 1.94\times 10^8 m/s$

(B)

Now we have to find out the wavelength of light in given medium.

We know that

                      $v= f \times \lambda$

                       $v \propto \lambda$

or

                       $v \propto \frac{1}{\mu}$

                       $\mu \propto \frac{1}{v \lambda}$

                       $\frac{\mu_a}{\mu_m} = \frac{\lambda_2}{\lambda_1}$                      [$\mu_a = 1$]

                      $\lambda_2 = \lambda_1 (\frac{\mu_a}{\mu_m} )$

                      $\lambda_2 = \frac{1\times 780nm}{1.55}$

                      $\lambda_2 = 503nm$

Thus, Wavelength of light in given medium $(\lambda_2) = 503nm$