A grating is made of exactly 8000 slits; the slit spacing is 1.50 μm . Light of wavelength 0.600

step 1 we know that d sine theta equals m lambda so m comes out to be g sine theta over lambda so m max

A grating is made of exactly 8000 slits; the slit spacing is...

A grating is made of exactly 8000 slits; the slit spacing is $1.50 \mu \mathrm{m} .$ Light of wavelength $0.600 \mu \mathrm{m}$ is incident normally on the grating. (a) How many maxima are seen in the pattern on the screen? (b) Sketch the pattern that would appear on a screen $3.0 \mathrm{~m}$ from the grating. Label distances from the central maximum to the other maxima.

Key Concepts

Determining the Total Number of Visible Maxima

By calculating the highest order m that satisfies the diffraction grating equation and then accounting for both positive and negative orders along with the central m = 0, one can determine the total number of maxima. This involves finding the maximum integer m for which the constructive interference condition is met and then using symmetry to count the fringes on both sides.

Angular to Linear Position Conversion

To translate the angular positions of the diffraction maxima into positions on a screen, the geometry of the setup is used. In many cases, for small angles, the approximation tan ? ? sin ? ? ? (in radians) is applied, allowing one to relate the angle to the linear displacement on the screen using the distance from the grating to the screen. This conversion is crucial for sketching and quantitatively labeling the observed diffraction pattern.

Diffraction Grating Equation

This fundamental equation, given by d sin ? = m?, relates the slit spacing (d), the angle of diffraction (?), the order number (m), and the wavelength of the light (?). It is used to predict the angular positions where constructive interference (bright fringes) will occur for a diffraction grating.

Diffraction Order

The diffraction order, represented by an integer m, designates the sequence of interference maxima. The central maximum corresponds to m = 0, and higher positive and negative integer values of m represent the positions of other bright fringes. The maximum possible order is determined by the condition |sin ?| ? 1, which limits m to values that satisfy m? ? d.

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