Answer to Question #88044 in Optics for Nicholas Legault

Question

Your teacher gives you a piece of cardboard with two pinholes on it, saying that they are separated by 205 μm ± 3%. In order to test this, you set up a double slit apparatus with the screen at a distance of 3.00 m away from the cardboard. You use a helium-neon laser (wavelength 638.2 nm) to generate an interference pattern. You measure the distance from the first to the seventh nodal line to be 56.9mm. Did your teacher give you accurate value for the separation of the pinholes?

Answer 1

The width of the interferential band is given by formula

$$Δ=\frac { \lambda L}{d} (1)$$

where d=205×10^-6 m, L=3 m, λ=638.2×10^-9 m

Using (1) we got: Δ=9.43×10^-3 m

In this case, the distance from the first to the seventh nodal line is equal to

$$9.43×10^ {-3 } m\times6 =56.58×10^{-3} m$$

Calculated value (56.58 mm) is agreed with experimental value (56.9 mm).

Answer:

The teacher gave accurate value for the separation of the pinholes.