Question

Light from a green laser pointer has a wavelength of 532 nm. The light illuminates two narrow slits separated by a distance d. The figure below shows the phasor diagram for a point P on a wall 2.00 m from the slits. The point Pis 21.4 cm from the central maximum and is located between the m=0 and m=1 maxima. The intensity of the light at Pis 2.67x10⁻⁶ W/m2. Through painstaking work and with incredible technological prowess, you add a third slit so that you now have three equally spaced identical slits with separation d. What is the intensity of the light at point P and at the central maximum?

Answer 1

The question examines how the intensity at a certain point on a screen changes when a third slit is added to a two-slit light interference setup. Accurate determination of the intensity with three slits requires applying the principles of multiple-slit interference using specific formulae, which relate intensity to the square of the number of slits.

Step-by-step explanation:

The question pertains to the concept of interference of light, specifically how adding a third slit to a double-slit setup (Young's double-slit experiment) affects the intensity of light at a particular point on a screen. In a multiple-slit interference scenario like this, the intensity on the screen for a point between two maxima is determined by both the interference and the diffraction pattern.

When a third slit of identical characteristics is added to a double-slit arrangement, maintaining an equal spacing of d between the slits, the resultant intensity patterns on the screen become sharper due to more constructive and destructive interference occurring with the additional path differences.

To determine the intensity at point P and the central maximum with three slits, one would typically apply the principles of multiple-slit interference, specifically using the formula for intensity distribution where I is proportional to the square of the number of slits times the single-slit intensity distribution.

However, without an exact formula or additional details on the initial phasor diagram mentioned in the question, a precise numerical answer cannot be provided. Understanding and applying such concepts require one to know the original intensity distribution with two slits and how the phasor diagram changes when an additional slit is introduced.