Question

A glass plate 2.50 mm thick, with an index of refraction of 1.65, is placed between a point source of light with wavelength 600 nm (in vacuum) and a screen. The distance from source to screen is 1.35 cm . How many wavelengths are there between the source and the screen?

Answer 1

25208.33

Step-by-step explanation:

Thickness of the glass plate 2.50mm = 2.50 × 10⁻³m

refractive index of the glass = 1.65

wavelength of the light in vaccum = 600nm

distance between source and screen = 1.35cm = 1.35 × 10⁻²m

wavelength of light in the medium

λ = 600 × 10⁻⁹ / 1.65

λ = 3.6364 × 10⁻⁷

number of wavelength in glass

`n_1 = (t)/(\lambda) \\\\n_1 = (2.50* 10^-^3)/(3.6364* 10^-^7)\\ \\n_1 = 6875`

Distance travel by light in air

D = d - t

D = 1.35 × 10⁻² - 2.50 × 10⁻³

D = 0.011m

Thus, the number of wavelength

`N_2=(D)/(\lambda)`

`N_2 =(0.011)/(600* 10^-^9) \\\\N_2 = 1833.33`

Total number of wavelength is

`N = N_1+N_2\\\\N = 6875+1833.33\\\\N = 25208.33`

Answer 2

Answer: 2.5*10^4

Step-by-step explanation:

The wavelength can be gotten using this formula

no of wavelength = d / λ

Also, the wavelength in a medium having a refraction index, n =

λ = λ(0) / n

so that, wavelength in the glass plate will be

λ = 600 / 1.65

λ = 363.64 nm

The thickness of glass plate is 2.5mm = 2.5*10^-3 m

The distance from source to screen is 1.35 cm = 0.0135 m

The distance between the source and screen, excluding the glass plate = 0.0135 - 0.0025 = 0.011 m

The number of wavelength is

(distance in air / wavelength in air) + (distance in glass / wavelength in glass) =

(0.011 / 600*10^-9) + (0.0025 / 363.63*10^-9) =

18333 + 6875 =

25208 = 2.5*10^4

Therefore, the total number of wavelength will be 2.5*10^4