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The second order bright fringe in a single slit diffraction pattern is 1.4 mm from the center. The screen is 80 cm from the slit of width 0.80 mm. Assuming monochromatic incident light calculate the wavelength of light.
Correct answer is '5600'. Can you explain this answer?
Verified Answer
The second order bright fringe in a single slit diffraction pattern is...
As in case of diffraction at single slit second order maximum is approximately midway between 2nd and 3rd diffraction minima,
.....(1)
and as for small q,   sin q = q = (y/D)....(2)
from equ.(1) and (2), we have

So    
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The second order bright fringe in a single slit diffraction pattern is...
Given:

Second order bright fringe = 1.4 mm

Distance from slit to screen = 80 cm

Width of slit = 0.80 mm

To find:

Wavelength of light

Formula used:

For single slit diffraction,

y = (mλL/d)

where y = distance from center to mth order bright fringe, λ = wavelength of light, L = distance from slit to screen, d = width of slit, m = order of fringe

Solution:

Using the formula,

y = (mλL/d)

For the second order bright fringe, m = 2

So, 1.4 mm = (2 × λ × 80 cm) / 0.80 mm

Simplifying, we get

λ = (1.4 mm × 0.80 mm) / (2 × 80 cm × 2)

λ = 5600 Å

Answer:

The wavelength of light is 5600 Å.
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The second order bright fringe in a single slit diffraction pattern is 1.4 mm from the center. The screen is 80 cm from the slit of width 0.80 mm. Assuming monochromatic incident light calculate the wavelength of light.Correct answer is '5600'. Can you explain this answer?
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