contestada

Monochromatic light of wavelength 491 nm illuminates two parallel narrow slits 6.93 μm apart. Calculate the angular deviation of the third-order (for m = 3) bright fringe (a) in radians and (b) in degrees.

Respuesta :

To solve this problem we will apply the concepts related to the double slit experiment. Here we test a relationship between the sine of the deviation angle and the distance between slit versus wavelength and the bright fringe order. Mathematically it can be described as,

[tex]dsin\theta = m\lambda[/tex]

Here,

d = Distance between slits

m = Any integer which represent the order number or the number of repetition of the spectrum

[tex]\lambda[/tex] = Wavelength

[tex]\theta[/tex] = Angular deviation

Replacing with our values we have,

[tex](6.93*10^{-6}) sin\theta = (3)(491*10^{-9})[/tex]

[tex]\theta = sin^{-1} (\frac{(3)(491*10^{-9}}{6.93*10^{-6}) })[/tex]

Part A)

[tex]\theta = 0.2141rad[/tex]

PART B)

[tex]\theta = 0.2141rad(\frac{360\°}{2\pi rad})[/tex]

[tex]\theta = 12.27\°[/tex]