A student holds a laser that emits light of wavelength 632.8 nm . The laser beam passes though a

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A student holds a laser that emits light of wavelength 632.8...

A student holds a laser that emits light of wavelength $632.8 \mathrm{nm} .$ The laser beam passes though a pair of slits separated by $0.300 \mathrm{mm},$ in a glass plate attached to the front of the laser. The beam then falls perpendicularly on a screen, creating an interference pattern on it. The student begins to walk directly toward the screen at $3.00 \mathrm{m} / \mathrm{s}$. The central maximum on the screen is stationary. Find the speed of the 50th-order maxima on the screen.

Key Concepts

Time Dependence of Interference Patterns

When elements of the experimental setup, such as the distance between the slits and the screen, change with time, the positions of the interference fringes shift accordingly. By differentiating the fringe position equation with respect to time, one can determine the rate at which a given fringe moves. This analysis is crucial for understanding dynamic interference effects when either the source or the observation screen is in motion.

Relationship Between Relative Motion and Fringe Shift

This concept examines how physical motion within the interference setup—such as the screen moving toward the slits—affects the observed fringe positions. The central maximum remains fixed due to symmetry, while higher order fringes shift at a rate that depends on the order number and the velocity of the moving component. Calculating the derivative of the fringe position with respect to time illustrates how the speed of fringe movement is linked to the motion of the screen or observer.

Young's Double-Slit Interference

This concept involves the formation of an interference pattern when coherent light passes through two closely spaced slits. The resulting pattern of bright and dark fringes arises from the constructive and destructive interference between the two light waves, with the condition for constructive interference being that the path difference between the waves is an integer multiple of the wavelength.

Fringe Position and the Small Angle Approximation

In a double-slit experiment, the position of the mth bright fringe on a screen is given by the formula y? = (m?L)/d, where m is the order of the maximum, ? is the wavelength, L is the distance from the slits to the screen, and d is the slit separation. When the angles involved are small, the approximation tan ? ? sin ? ? ? (in radians) is used to simplify the relationship between the fringe position and the geometry of the setup.

Transcript

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