Question

In the Young's double slit experiment the intensity produced by each one of the individual slits is \(I_0\). The distance between two slits is \(2\,\text{mm}\). The distance of screen from slits is \(10\,\text{m}\). The wavelength of light is \(6000\,\text{\AA}\). The intensity of light on the screen in front of one of the slits is ________.

• A. \( I_0 \)
• B. \( 2I_0 \)
• C. \( \dfrac{I_0}{2} \)
• D. \( 4I_0 \)

Hint:

Maximum or minimum interference occurs only at points equidistant from both slits.

Answer 1

The Correct Option is A

The Young's double slit experiment is a classic physics experiment that demonstrates the principle of interference of light waves. In this setup, two coherent light sources (slits) create an interference pattern on a screen.

Given:

• Intensity of light from each slit, \(I_0\)
• Distance between slits, \(d = 2\,\text{mm} = 2 \times 10^{-3}\,\text{m}\)
• Distance from slits to screen, \(D = 10\,\text{m}\)
• Wavelength of light, \(\lambda = 6000\,\text{\AA} = 6000 \times 10^{-10}\,\text{m}\)

To find the intensity on the screen in front of one of the slits, we need to consider the interference pattern produced by these slits. The intensity at any point on the screen due to interference is given by:

\(I = I_0 + I_0 + 2 \sqrt{I_0 \cdot I_0} \cos \phi\)

Where \(\phi\) is the phase difference between the light waves from the two slits. On the screen directly in front of one slit, there is no path difference, and the phase difference \(\phi\) is zero.

Thus, the cosine term becomes:

\(\cos \phi = \cos 0 = 1\)

Substituting this into the intensity equation:

\(I = I_0 + I_0 + 2 \sqrt{I_0 \cdot I_0} \cdot 1 = 2I_0 + 2I_0 = 4I_0\)

This would be the case if we consider the point directly between both slits on the screen, where the interference is constructive.

However, if we focus on the point directly in front of one slit, no interference from the other slit should be considered. Therefore, only the intensity from that single slit contributes to the intensity:

Thus, the intensity directly in front of one slit should indeed be \(I_0\).

Correct Option: \(I_0\)