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Chapter 33: Q. 50 (page 957)

FIGURE P33.49 shows the interference pattern on a screen 1.0mbehind a diffraction grating. The wavelength of the light is 620nm. How many lines per millimeter does the grating have?

Short Answer

Expert verified

The grating hasn=645nmof lines per millimetre.

Step by step solution

01

Step: 1 Derivating:

The bright fringes diffraction grating as

dsin⁡θm=mλd=mλsin⁡θmd=λsin⁡θ1.

02

Step: 2 Finding the angle:

The place of bright fringes as

tan⁡θ1=y1Lθ1=tan−1⁡y1Lθ1=tan−1⁡43.6cm100cmθ1=23.56∘.

03

Step: 3 Calculating grating value:

The spacing and grating value as

d=620×10−9msin⁡23.56∘d=1.55×10−6md=1.55×10−3mm.

The number of lines is

n=11.55×10−3mmn=645.

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Most popular questions from this chapter

a. Green light will shine through a hole with a 100-mm-diameter hole of and is seen on a screen. Does the circular point of lights 20%,is on the screen shrink in diameter, rise in diameter, or remain the same in diameter by? Explain.

b. Green light will shine through a hole with a 100-μmdiameter of and is seen on a screen. Does the circular point of lights is 20%,on the screen shrink in diameter, rise in diameter, or remain the same in diameter by? Explain.

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?

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The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are 656nm (red) and 486nm (blue). Light from a hydrogen lamp illuminates a diffraction grating with 500lines/mm, and the light is observed on a screen 1.50m behind the grating. What is the distance between the first-order red and blue fringes?
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