Consider a beam of light of wavelength 'λ' incident on ...
When half-wave plate is introduced, the plane of polarization is rotated by
Since intensity o f light analyzer is zero, plane o f polarization rotates by an angle 45
0.
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Consider a beam of light of wavelength 'λ' incident on ...
Λ = 500 nm (nanometers) passing through a narrow slit of width d = 0.1 mm (millimeters). The diffraction pattern produced by the slit can be analyzed using the principles of wave optics.
Diffraction occurs when a wave encounters an obstacle or aperture that is comparable in size to its wavelength. In this case, the wavelength of the light is 500 nm, which is in the visible range of the electromagnetic spectrum. The narrow slit has a width of 0.1 mm, which is larger than the wavelength of the light.
When light passes through a narrow slit, it spreads out and creates a diffraction pattern on a screen or surface placed behind the slit. This pattern consists of alternating bright and dark fringes, known as interference fringes.
The spacing between the fringes in the diffraction pattern can be calculated using the formula:
sin(θ) = mλ / d
Where:
- θ is the angle between the direction of the incident beam and the direction of the m-th order fringe.
- m is the order of the fringe (m = 0 for the central maximum, m = ±1 for the first-order fringes, m = ±2 for the second-order fringes, and so on).
- λ is the wavelength of the light.
- d is the width of the slit.
Using this formula, we can calculate the angle θ for the first-order fringe (m = ±1):
sin(θ) = (±1)(500 nm) / (0.1 mm)
θ = sin^(-1)(±1)(500 nm) / (0.1 mm)
The value of sin^(-1)(x) gives the angle whose sine is x. So we can solve this equation to find the value of θ.
Once we have the angle θ, we can calculate the spacing between the fringes using the formula:
dθ = λ / d
Where:
- dθ is the spacing between the fringes.
- λ is the wavelength of the light.
- d is the width of the slit.
Using the values given, we can substitute them into the formula to find the spacing between the fringes.
It's important to note that this calculation assumes the light is passing through a single narrow slit. If there are multiple slits or other factors affecting the diffraction pattern, the calculations may be more complex.