A set of narrow vertical slits is located a distance D from a screen. The slits

Question

A set of narrow vertical slits is located a distance D from a screen. The slits are equally spaced and have the same width. The intensity pattern in the figure is observed when light from a laser passes through the slits, illuminating them uniformly. The screen is perpendicular to the direction of the light. Data: Distance to the screen = 2.23 m, Wavelength of light = 570 nm, Distance between tick marks on the intensity figure = 1.10 cm.

What is the spacing between the slits?

Calculate the width of the slits.

If the slit separation is increased by a factor of 4, what would be the distance between the principal peaks on the screen?

Explanation / Answer

The central pattern can be seen as a di raction pattern from a single slit repeating itself. Estimate the
first minimum for such pattern. This would be approximately x = 5x = 5 X 1.1 = 5.5cm

The angle (theta) can be found as
tan(theta) = x/L = 0.055/2.23
= 0.0247

(theta)= 1.415 degree

For the first minimumm m = 1 for single slit difraction

a sin( heta)= m (lambda)

a= 1 X 560 X 10^-9 / sin(1.415)

= 5.67 X 10^-7 m

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