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Chapter 36: Q94P (page 1115)

A diffraction grating 1.00 cm wide has 10 000 parallel slits. Monochromatic light that is incident normally is diffracted through 30° in the first order. What is the wavelength of the light?

Short Answer

Expert verified

The wavelength of light is 500 nm.

Step by step solution

01

Identification of given data

The given data can be listed below,

  • The width of the diffraction grating is,D=1.00cm
  • The number of slits used in grating are,N=10000
  • The angle of diffraction is,θ=30°
02

Concept/Significance of wavelength

The separation between two successive wave crests or troughs is known as a wavelength. It is determined by measuring the wave's direction.

03

Determination of the wavelength of the light

The separation of slits is given by,

d=DN

Here,D is the width grating and N is the number of slits.

According to brag’s law, the wavelength of the light is given by,

dsinθ=mλλ=DsinθNm

Substitute all the values in the above,

λ=1.0×107nmsin30°1×10000=500nm

Thus, the wavelength of light is 500 nm.

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