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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 2.0渭mapart, what is the first-order diffraction angle for green light 位=550nm?

Short Answer

Expert verified

For green light, the first-order diffraction angle is胃m=16鈭�.

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鈦�胃m=m位

The angle of mthfringe is there

sin鈦�胃m=m位d胃m=sin鈭�1鈦�m位d

03

Step: 3 Diffraction angle for green light:

The angle of light by

胃m=sin鈭�1鈦�1脳5.50脳10鈭�72脳10鈭�6胃m=sin鈭�1鈦�(0.275)胃m=16鈭�.

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Most popular questions from this chapter

Helium atoms emit light at several wavelengths. Light from a helium lamp illuminates a diffraction grating and is observed on a screen50.00cmbehind the grating. The emission at wavelength 501.5nmcreates a first-order bright fringe 21.90cmfrom the central maximum. What is the wavelength of the bright fringe that is 31.60cmfrom the central maximum?

White light400-700nmincident on a 600line/mmdiffraction grating produces rainbows of diffracted light. What is the width of the first-order rainbow on a screen 2.0mbehind the grating?

A Michelson interferometer operating at a 600nmwavelength has a 2.00-cm-long glass cell in one arm. To begin, the air is pumped out of the cell and mirror M2is adjusted to produce a bright spot at the center of the interference pattern. Then a valve is opened and air is slowly admitted into the cell. The index of refraction of air at 1.00atmpressure is 1.00028. How many brightdark-bright fringe shifts are observed as the cell fills with air?

3. FIGURE Q33.3 shows the viewing screen in a double-slit experiment. FringeCis the central maximum. What will happen to the fringe spacing if

a. The wavelength of the light is decreased?

b. The spacing between the slits is decreased?

c. The distance to the screen is decreased?

d. Suppose the wavelength of the light islocalid="1649170567955" 500nm. How much farther is it from the dot on the screen in the center of fringe E to the left slit than it is from the dot to the right slit?

A double-slit experiment is set up using a helium-neon laser (位=633nm). Then a very thin piece of glass (n=1.50) is placed over one of the slits. Afterward, the central point on the screen is occupied by what had been the m=10 dark fringe. How thick is the glass?
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