When blue light with a wavelength of 465 nm illuminates a...

Name: Problem 74, Chapter 28: Physics
Uploaded: 2021-03-27T12:43:08-08:00
Duration: 3 min 5 s
Channel: Khoobchandra Agrawal
Description: When blue light with a wavelength of 465 nm illuminates a diffraction grating, it produces a first-order principal maximum but no second-order maximum. (a) Explain the absence of higher-order principal maxima. (b) What is the maximum spacing between lines on this grating?

When blue light with a wavelength of 465 nm illuminates a diffraction grating, it produces a first-order principal maximum but no second-order maximum. (a) Explain the absence of higher-order principal maxima. (b) What is the maximum spacing between lines on this grating?

Key Concepts

Diffraction Grating

A diffraction grating is an optical component with a regular pattern (such as numerous parallel slits or lines) that splits and diffracts light into several beams traveling in different directions. The bright spots, known as principal maxima, arise from the constructive interference of light waves scattered from the individual openings, and their positions are determined by the grating’s spacing and the wavelength of the light.

Interference Condition for Maxima

The principal maxima in a diffraction grating occur when the path difference between adjacent slits is an integer multiple of the wavelength. This condition is mathematically expressed as d sin(?) = m?, where d is the spacing between slits, ? is the angle of diffraction, ? is the wavelength, and m is the order number of the maximum. This equation governs the formation and angular position of each maximum.

Angular Limits on Diffraction Orders

For the interference condition d sin(?) = m? to yield a physical (real) angle, the sine of the diffraction angle must be less than or equal to 1. This requirement, sin(?) ? 1, imposes a limit on the possible order number m for a given wavelength and grating spacing. If m? exceeds d, sin(?) would have to be greater than 1, making the corresponding order nonexistent. This is why higher orders may be absent when the spacing is small compared to multiples of the wavelength.

Grating Spacing and Order Suppression

The relation between the grating spacing and the existence of higher diffraction orders is critical. To observe a particular maximum order m, the condition m? ? d must be met. If the grating spacing is such that the next higher order, say m+1, would require sin(?) > 1, then that order (and higher orders) will not form. This sets an upper limit on the spacing d for ensuring that only desired orders (e.g., the first order) are visible.

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