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Two narrow slits are illuminated by light of wavelength λ. The slits are spaced 20 wavelengths apart. What is the angle, in radians, between the central maximum and the m = 1 bright fringe?

Respuesta :

Answer:

the angle, in radians, between the central maximum = 2.87degree or 0.05radians

Explanation:

The detailed steps and appropriate formula is as shown in the attachment.

Using λm = dsin teta

where d =20λ, m = 1

from the formula, sin teta = λ/20λ

= sin teta = 0.05

teta = arc sin(0.05) = 2.87 degree

Ver imagen olumidechemeng
Lanuel

The angle (in radians) between the central maximum and the m = 1 bright fringe is 0.0201 rad.

Given the following data:

  • Distance between slits = 20[tex]\lambda[/tex]
  • Order of bright fringe, m = 1

To determine the angle (in radians) between the central maximum and the m = 1 bright fringe, we would apply an interference experiment formula:

Mathematically, an interference experiment is given by the formula:

[tex]dsin\theta =m \lambda[/tex]

Where:

  • d is the distance between slits.
  • m is the order of fringe.
  • [tex]\lambda[/tex] is the wavelength.
  • [tex]\theta[/tex] is the angle between bright fringe.

Making [tex]\theta[/tex] the subject of formula, we have:

[tex]\theta = sin^{-1}(\frac{m\lambda}{d} )[/tex]

Substituting the given parameters into the formula, we have;

[tex]\theta = sin^{-1}(\frac{1\; \times \;\lambda}{20\lambda} )\\\\\theta = sin^{-1}(\frac{1}{20})\\\\\theta = sin^{-1}(0.05)\\\\\theta = 2.87^\circ[/tex]

Angle = 2.87°

Angle in radians:

[tex]2.87 \times \frac{\pi}{180} = 0.0501 \; rads[/tex]

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