A slit has a width of W_1 = 4.3 times 10^-6 m. When light with a wavelength of l

Question

A slit has a width of W_1 = 4.3 times 10^-6 m. When light with a wavelength of lambda_1 = 541 nm passes through this slit, the width of the central bright fringe on a flat observation screen has a certain value. With the screen kept in the same place, this slit is replaced with a second slit (width W_2), and a wavelength of lambda_2 = 409 nm is used. The width of the central bright fringe on the screen is observed to be unchanged. Find W_2. W_2 = For a wavelength of 420 nm, a diffraction grating produces a bright fringe at an angle of 26 degree. For an unknown wavelength, the same grating produces a bright fringe at an angle of 44 degree. In both cases the bright fringes are of the same order m. What is the unknown wavelength? nm

Explanation / Answer

1)

The angular deflection equation is theta = arcsin(m/a) where a is the slit width.

Thus theta doesn't change if m and /a are constant.

So 1/W1 = 2/W2,

W2 = W12/1.

W2 = (4.3 x 10^-6 x 409 x 10^-9 m) / (541 x 10^-9 m)

W2 = 3.25 x 10^-6 m

2)

= 420 nm, = 26°, ' = 47°, ' = ?

dsin = m, dsin' = m'
so

sin/sin' = /'

' = sin'/sin = 420*sin(44°)/sin(26°) = 665.7nm

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