A parallel beam of light of diameter 1.8 cm contains two wavelengths 4999.75 Åand 5000.25 Å. The light is incident perpendicularly on a large diffraction grating with 5000 lines per centimeter. Using Rayleigh criterion, find the least order at which the two wavelengths are resolved.Correct answer is '2'. Can you explain this answer?

Question

A parallel beam of light of diameter 1.8 cm contains two wavelengths 4999.75 &Aring;and 5000.25 &Aring;. The light is incident perpendicularly on a large diffraction grating with 5000 lines per centimeter. Using Rayleigh criterion, find the least order at which the two wavelengths are resolved.Correct answer is '2'. Can you explain this answer?

Answer

And 5000.25 Ångstroms. The distance between the first and third bright fringes on a screen placed perpendicular to the beam and at a distance of 1.5 meters from the source will be:

We can use the formula for the distance between fringes in a double-slit experiment:

d sin(theta) = m lambda

where d is the distance between the slits, theta is the angle of the fringe measured from the central maximum, m is the order of the fringe (m=1 for the first bright fringe), and lambda is the wavelength of the light.

For a parallel beam of light, we can assume that the angle theta is very small and can be approximated by theta = y/L, where y is the distance from the central maximum to the fringe and L is the distance from the slits to the screen.

Since we have two wavelengths, we need to calculate the distance between fringes for each wavelength separately and then take the difference.

For lambda = 4999.75 Ångstroms:

d sin(theta) = m lambda

d sin(y/L) = lambda

y = L sin^-1(lambda/d)

y = 1.5 sin^-1(4999.75/0.18x10^-3)

y = 1.5 x 0.0276 radians

y = 0.0414 meters

For lambda = 5000.25 Ångstroms:

y = 1.5 sin^-1(5000.25/0.18x10^-3)

y = 1.5 x 0.0277 radians

y = 0.0416 meters

The difference between these two distances is:

0.0416 - 0.0414 = 0.0002 meters

Therefore, the distance between the first and third bright fringes for these two wavelengths is 0.0002 meters.

Similar GATE Doubts

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?

Top Courses for GATE

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Other Engg Branches

Related Exams

Company