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A diffraction grating of width 42mm has 12000 lines.Monochromatic light is incid...

Apr 20, 2024

A diffraction grating of width 42mm has 12000 lines.Monochromatic light is incident normally on the grating.The angle between the two second-order diffraction maxima is 41.4 degrees.Calculate the wavelength of the incident light.

Answer

The wavelength of the incident light is 587.6 nm.

Solution

Use the diffraction grating formula:

d \sin \theta = m \lambda

, where

d

is the grating spacing,

\theta

is the diffraction angle,

m

is the order of the maximum, and

\lambda

is the wavelength

Calculate the grating spacing

d

: Given the width of the grating

W = 42

mm and the number of lines

N = 12000

, the spacing is

d = \frac{W}{N}

Convert the angle between the second-order maxima to the angle for one maximum: The angle for one maximum

\theta

is half of the given angle, so

\theta = \frac{41.4^\circ}{2}

Calculate the wavelength

\lambda

: Using the formula from step a, with

m = 2

for the second-order maximum, solve for

\lambda

Key Concept

Diffraction grating formula

Explanation

The diffraction grating formula relates the angle of diffraction maxima to the wavelength of light and the spacing between the grating lines. By knowing the grating spacing and the angle for a specific order of maximum, the wavelength can be calculated.