Question

36.4 diffraction by a double slit
a blue laser is incident on a pair of double slits, creating an interference pattern a distance of 4.0 m away. if you wish to make the spacing of the spots in the pattern closer together,

• increase the distance between the two slits.
• replace the blue laser with a violet laser.
• replace the blue laser with a red laser.
• decrease the distance between the two slits.

Explanation:

The formula for the fringe spacing (\(\Delta y\)) in double - slit interference is \(\Delta y=\frac{\lambda L}{d}\), where \(\lambda\) is the wavelength of the light, \(L\) is the distance from the slits to the screen, and \(d\) is the distance between the two slits. To make the spacing of the spots (fringe spacing) closer together (decrease \(\Delta y\)), we can either decrease \(\lambda\) or increase \(d\) (since \(L\) is fixed here).

• For the option "Increase the distance between the two slits (\(d\))": From the formula \(\Delta y=\frac{\lambda L}{d}\), if \(d\) increases, \(\Delta y\) will decrease (the spots get closer together).
• For "Replace the blue laser with a violet laser": Violet light has a shorter wavelength than blue light. But a shorter wavelength would make \(\Delta y\) smaller, but let's check other options.
• For "Replace the blue laser with a red laser": Red light has a longer wavelength than blue light. Using the formula, a longer \(\lambda\) would increase \(\Delta y\) (spots get farther apart), so this is incorrect.
• For "Decrease the distance between the two slits (\(d\))": Decreasing \(d\) would increase \(\Delta y\) (spots get farther apart), so this is incorrect.

Among the options, increasing the distance between the two slits will decrease the fringe spacing (make the spots closer together).

Answer:

A. Increase the distance between the two slits.