A diffraction grating is a square 1.0 cm on a side and...

A diffraction grating is a square $1.0 \mathrm{cm}$ on a side and contains 3000 slits. What is the angle of the first intensity maximum in the diffraction pattern with blue light $(\lambda=450 \mathrm{nm}) ?$

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Key Concepts

Diffraction Grating

A diffraction grating consists of a large number of equally spaced slits that diffract light. When light waves pass through the slits, they interfere constructively and destructively, leading to a pattern of bright and dark regions (maxima and minima) on a screen. The grating enhances the separation of different wavelengths, which is fundamental in spectroscopic applications.

Grating Equation

The grating equation, given by d sin(?) = m?, relates the slit separation (d), the wavelength of the incident light (?), and the order of the maximum (m) to the angle (?) at which a constructive interference maximum occurs. This formula is essential for predicting and analyzing the angular positions of the intensity maxima produced by the diffraction grating.

Slit Spacing Determination

Determining the spacing between the slits is crucial when applying the grating equation. If the total number of slits and the physical size of the grating are known, the spacing d can be calculated by dividing the total length by the number of slits. This step allows for the correct application of the grating equation to find the angle for a specific order of maximum.

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