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Chapter 33: Q. 52 (page 957)

The wings of some beetles have closely spaced parallel lines of melanin, causing the wing to act as a reflection grating. Suppose sunlight shines straight onto a beetle wing. If the melanin lines on the wing are spaced 2.0μmapart, what is the first-order diffraction angle for green light λ=550nm?

Short Answer

Expert verified

For green light, the first-order diffraction angle isθm=16∘.

Step by step solution

01

Step: 1 Diffraction angle:

The smaller the value of d for a given order and wavelength, the higher the diffraction angle. To put it another way, the greater the number of slits per metre, the greater the diffraction angle.

02

Step: 2 Finding angle:

By grating equation,

dsin⁡θm=mλ

The angle of mthfringe is there

sin⁡θm=mλdθm=sin−1⁡mλd

03

Step: 3 Diffraction angle for green light:

The angle of light by

θm=sin−1⁡1×5.50×10−72×10−6θm=sin−1⁡(0.275)θm=16∘.

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Most popular questions from this chapter

FIGURE P33.56 shows the light intensity on a screen behind a single slit. The slit width is 0.20mmand the screen is 1.5mbehind the slit. What is the wavelength (in nm) of the light?

a. Green light shines through a 100-mm-diameter hole and is observed on a screen. If the hole diameter is increased by 20%, does the circular spot of light on the screen decrease in diameter, increase in diameter, or stay the same? Explain.

b. Green light shines through a 100−μm-diameter hole and is observed on a screen. If the hole diameter is increased by20%, does the circular spot of light on the screen decrease in diameter, increase in diameter, or stay the same? Explain.

FIGUREP33.36shows the light intensity on a screen behind a double slit. The slit spacing is 0.20mmand the wavelength of the light is 620nm. What is the distance from the slits to the screen?

A diffraction grating is illuminated simultaneously with red light of wavelength660nmand light of an unknown wavelength. The fifth-order maximum of the unknown wavelength exactly overlaps the third-order maximum of the red light. What is the unknown wavelength?

Light from a helium-neon laser (λ=633nm)illuminates a circular aperture. It is noted that the diameter of the central maximum on a screen 50cmbehind the aperture matches the diameter of the geometric image. What is the aperture's diameter (in mm)?
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