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Chapter 33: Q.55 (page 957)

A diffraction grating has slit spacing d. Fringes are viewed on a screen at distance L. Find an expression for the wavelength of light that produces a first-order fringe on the viewing screen at distanceLfrom the center of the screen.

Short Answer

Expert verified

The wavelength of light is位=d22.

Step by step solution

01

Step: 1 Diffraction grating:

A light beam is created by scratching a flat piece of transparent material with multiple parallel scratches. The material may be scratched with a great number of scratches per centimetre.

02

Step: 2 Angle:

The mthfringe as

Ym=Ltan鈦�胃m,胃=tan鈭�1鈦�YL

03

Step: 3 Obtaining wavelength:

The wavelength from grating equation as

dsin鈦�胃m=m位位=dsin鈦�胃1位=d22.

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Most popular questions from this chapter

Two 50-渭m-wide slits spaced 0.25mmapart are illuminated by blue laser light with a wavelength of 450nm. The interference pattern is observed on a screen2.0m behind the slits. How many bright fringes are seen in the central maximum that spans the distance between the first missing order on one side and the first missing order on the other side?

It shows the light intensity on a viewing screen behind a circular aperture. What happens to the width of the central maximum if the

a. The wavelength of the light is increased.

b. The diameter of the aperture is increased.

c. How will the screen appear if the aperture diameter is less than the light wavelength?

A Michelson interferometer using 800nm light is adjusted to have a bright central spot. One mirror is then moved 200nm forward, the other 200nm back. Afterward, is the central spot bright, dark, or in between? Explain.

A 600 line/mm diffraction grating is in an empty aquarium tank. The index of refraction of the glass walls is nglass=1.50. A helium-neon laser (位=633nm)is outside the aquarium. The laser beam passes through the glass wall and illuminates the diffraction grating.

a. What is the first-order diffraction angle of the laser beam?

b. What is the first-order diffraction angle of the laser beam after the aquarium is filled with water nwater=1.33?

FIGURE shows the light intensity on a viewing screen behind a circular aperture. What happens to the width of the central maximum if

a. The wavelength of the light is increased?

b. The diameter of the aperture is increased?

c. How will the screen appear if the aperture diameter is less than the light wavelength?
See all solutions

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