Question

A glass plate 3.45 mm thick, with an index of refraction of 1.60, is placed between a point source of light with wavelength 500 nm (in vacuum) and a screen. The distance from source to screen is 2.05 cm. How many wavelengths are there between the source and the screen?

Answer 1

Answer:

$4.51\times 10^4$

Explanation:

We are given that

Thickness of glass plate=3.45 mm=$3.45\times 10^{-3}m$

Using $1mm=10^{-3} m$

Refractive index=$n=1.6$

Wavelength in air, $\lambda_0=500nm=500\times 10^{-9} m$

$1 nm=10^{-9} m$

Distance from source to screen=d=2.05 cm=$2.05\times 10^{-2} m$

$1 cm=10^{-2} m$

Wavelength in medium=$\lambda=\frac{\lambda_0}{n}$

Using the formula

Wavelength in medium=$\lambda=\frac{500\times 10^{-9}}{1.6}=312.5\times 10^{-9} m$

Distance between source and scree except glass plate=$2.05\times 10^{-2}-3.45\times 10^{-3}=17.05\times 10^{-3} m$

Number of wavelength=$\frac{distance];in\;air}{wavelength\;in\;air}+\frac{distance\;in\;glass}{wavelength\;in\;glass}$

Number of wavelength=$\frac{17.05\times 10^{-3}}{500\times 10^{-9}}+\frac{3.45\times 10^{-3}}{312.5\times 10^{-9}}$

Number of wavelength=$4.51\times 10^4$