Question

White light is spread out into its spectral components by a diffraction grating. If the grating has 2,090 grooves per centimeter, at what angle (in degrees) does red light of wavelength 640 nm appear in first order

Answer 1

Main answer: 7.68

Supporting answer: Diffraction

Diffraction of light is the phenomenon where the bending of light happens around corners such that it spreads out and illuminates areas where the formation of shadow is expected.

The diffraction of light is divided into two types:

• Fresnel diffraction: Here the division of light is from a point source and incident and diffracted wavelengths are spherical
• Fraunhoffer diffraction: Here the division of light is from a point source or multiple source and incident and diffracted wavelengths are parallel.

Here diffraction grating, is defined as an optical element that divides the light into various wavelengths.

The formula for diffraction is: dsinФ=nλ

where, d is the distance between the slits, Ф is the diffracting angle, n is the order number and λ is the wavelength.

Given, grating is 2090 grooves per centimeter for n=1,

d=n/λ

Then,

$d=\frac{1*10^{-2} }{2090} \\d=4.78*10^{-6}m$

Therefore,

dsinФ=nλ

sinФ=nλ/d

$=\frac{1*640*10^{-9} }{4.78*10^{-6} } \\=133.89*10^{-3} \\=0.1338$

Ф=

$=sin^{-1} (0.1338)\\=7.68$

Therefore, the red light appears at an angle of 7.68

You can also refer,

https://brainly.in/question/40622849

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