Question

A slit 1.00 mm wide is illuminated by light of wavelength 589 nm. The diffraction pattern is seen on a screen 3.00 m away. What is the distance between the first two diffraction minima on the same side of the central diffraction maximum?

Answer 1

The distance between the first two diffraction minima on the same side of the central diffraction maximum can be calculated using the formula d*sin(theta) = m*lambda. Using the given values, the distance is approximately 1.86 m.

Step-by-step explanation:

The distance between the first two diffraction minima on the same side of the central diffraction maximum can be calculated using the formula:

d*sin(theta) = m*lambda

Where d is the width of the slit, theta is the angle between the diffracted light and the central axis, m is the order of the minima, and lambda is the wavelength of light.

In this case, we are interested in the first minima, so m = 1. We can rearrange the formula to solve for the angle:

theta = arcsin(m*lambda / d)

Substituting the given values, we get:

theta = arcsin((1 * 589 nm) / 1.00 mm) = arcsin(589 / 1000) = arcsin(0.589)

Using a trigonometric calculator, we find that the angle is approximately 35.31 degrees.

Since the screen is 3.00 m away, the distance between the first two diffraction minima is given by:

distance = screen distance * tan(theta)

Substituting the values, we get:

distance = 3.00 m * tan(35.31 degrees) = 1.86 m