Question

For a demonstration, a professor uses a razor blade to cut a thin slit in a piece of aluminum foil. When she shines a laser pointer (λ=680nm) through the slit onto a screen 5.6 m away, a diffraction pattern appears. The bright band in the center of the pattern is 8.1 cm wide.
1. What is the width of the slit? answer in mm.

Answer 1

Answer:

Slit width is 0.109 mm

Solution:

As per the question:

Wavelength of the light, $\lambda = 680\ nm = 680\times 10^{- 9}\ m$

Distance from the screen, D = 5.6 m

Bright band in the center, 2x = 8.1 cm

x = 4.05 cm

Now,

To calculate the slit width, w:

From the diffraction:

$sin\theta = \frac{\lambda}{w}$

For small angle:

$sin\theta$ ≈ $tan\theta = \frac{x}{D}$

Also

$\frac{x}{D} = \frac{\lambda }{w}$

Thus

$w = \frac{D}{x}\times \lambda$

Substituting appropriate values in the above eqn:

$w = \frac{6.5}{4.05\times 10^{-2}}\times 680\times 10^{- 9}$

w = 0.109 mm