Question

When a light of wavelength 5000 angstrom in vacuum travels through Same thickness in glass and water,the difference in the number of waves is 400.Find thickness.(Refractive indices of glass and water are 3/2 and 4/3 respectively).

Answer 1

Answer:

The thickness is 1.2 mm

Explanation:

Let the thickness be L

Wave length of the wave $\lambda=5000$ Angstrom

We know that wavelength of a wave in medium of refractive index n is given by

$\boxed{\lambda'=\frac{\lambda}{n}}$

Where $\lambda$ is wavelength in air

Thus,

wavelength in glass

$\lambda_g=\frac{5000}{3/2}$

$\implies \lambda_g=\frac{10000}{3}$

Similarly wavelength in water

$\lambda_w=\frac{5000}{4/3}=\frac{15000}{4}$

Also,

Number of waves = Distance/Wavelength

Number of waves in glass - No. of waves in water = 400

$\implies \frac{L}{\lambda_g}-\frac{L}{\lambda_w}=400$

$\implies L(\frac{1}{\lambda_g}-\frac{1}{\lambda_w})=400$

$\implies L(\frac{3}{10000}-\frac{4}{15000})=400$

$\implies L(\frac{18-16}{60000})=400$

$\implies L(\frac{2}{60000})=400$

$\implies L=400\times\frac{60000}{2}$

$\implies L=200\times 60000$

$\implies L=12\times 10^6$ Angstrom

$\implies L=12\times 10^{-4}$ m

$\implies L=1.2$ mm

Hope this helps.