Answer:
There are 2.71x10⁴ wavelengths between the source and the screen.
Explanation:
The number of wavelengths (N) can be calculated as follows:
[tex] N = \frac{d_{g}}{\lambda_{g}} + \frac{d_{a}}{\lambda_{a}} [/tex]
Where:
[tex]d_{g}[/tex]: is the distance in glass = 2.25 mm
[tex]d_{a}[/tex]: is the distance in air = 1.50 cm - 0.225 cm = 1.275 cm
[tex]\lambda_{g}[/tex]: is the wavelength in glass
[tex]\lambda_{a}[/tex]: is the wavelength in air = 620 nm
To find the wavelength in glass we need to use the following equation:
[tex] n_{g}*\lambda_{g} = n_{a}*\lambda_{a} [/tex]
Where:
[tex]n_{g}[/tex]: is the refraction index of glass = 1.80
[tex]n_{a}[/tex]: is the refraction index of air = 1
[tex] \lambda_{g} = \frac{\lambda_{a}}{n_{g}} = \frac{620 nm}{1.80} = 344.4 nm [/tex]
Hence, the number of wavelengths is:
[tex] N = \frac{d_{g}}{\lambda_{g}} + \frac{d_{a}}{\lambda_{a}} [/tex]
[tex] N = \frac{2.25 \cdot 10^{-3} m}{344.4 \cdot 10^{-9} m} + \frac{1.275 \cdot 10^{-2} m}{620 \cdot 10^{-9} m} [/tex]
[tex] N = 2.71 \cdot 10^{4} [/tex]
Therefore, there are 2.71x10⁴ wavelengths between the source and the screen.
I hope it helps you!
