Light of 650 nm is incident on two slits. A maximum is seen...

Light of $650 \mathrm{~nm}$ is incident on two slits. A maximum is seen at an angle of $4.10^{\circ}$ and a minimum of $4.78^{\circ}$. What is the order $m$ of the maximum and what is the distance $d$ between the slits?

Key Concepts

Double-Slit Interference

This is the phenomenon where two coherent light sources (or slits) produce overlapping waves that interfere with each other. The interference leads to a pattern of alternating bright and dark regions on a screen due to constructive and destructive interference, respectively. This concept is fundamental in demonstrating the wave nature of light.

Constructive Interference

Constructive interference occurs when the phase difference between waves leads to their amplitudes adding coherently, producing bright fringes in an interference pattern. The condition for constructive interference in a double-slit experiment is given by d sin? = m?, where d is the distance between the slits, ? is the angle of the maximum, m is an integer representing the order of the maximum, and ? is the wavelength of the light.

Destructive Interference

Destructive interference happens when the phase difference causes the waves to cancel each other out, resulting in dark fringes. For a two-slit experiment with equal intensity sources, the condition for a minimum (complete cancellation) is usually given by d sin? = (m + 1/2)?, where the additional half-wavelength phase difference ensures that the peaks of one wave align with the troughs of the other.

Order of Maximum

The order of a maximum (denoted by m) indicates how many wavelengths fit into the path difference between the two slits at a given angle. This integer not only labels the bright fringes but also plays a crucial role in determining other parameters of the interference setup, such as the slit separation when combined with the wavelength and measured angle.

Determining Slit Separation

By applying the equations for interference, one can use the measured angular positions of the bright and dark fringes along with the known wavelength to calculate the distance between the slits (d). The relationship d = m?/sin? for bright fringes, for example, provides a direct method to determine d when the order m and the corresponding angle ? are known.

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