Question

In the Young's double slit experiment, the intensity of light at a point on the screen where the path difference $\lambda$ is K,( $\lambda$ being the wavelength of light used). The intensity at a point where the path difference is ${\lambda}/4 $ will be

• A. K
• B. K/4
• C. K/2
• D. zero

Answer 1

The Correct Option is C

Intensity at any point on the screen is 
\(I= 4 I_0 {cos}^ 2 \frac{\Phi }{2}\) 
where \(I_0\) is the intensity of either wave and \(\Phi\) is the 
phase difference between two waves. 
Phase difference, \(\Phi = \frac{2 \pi}{\lambda} \times\) Path difference 
When path difference is \(\lambda\), then 
\(\Phi = \frac{ 2 \pi }{ \lambda } \times \lambda = 2 \pi\)
\(\therefore \, \, \, I = 1 I_0 {cos} ^2 \bigg( \frac{2 \pi}{2} \bigg) = 4 I_0 {cos }^2(\pi) = 4 I_0 =K\) ....(i) 
When path difference is \(\frac{\lambda}{ 4}\) , then 
\(\Phi = \frac{ 2 \pi }{ \lambda } \times \frac{\lambda}{ 2}\)
\(\therefore \, \, \, I =4 I_0 {cos}^2 \bigg( \frac{ \pi}{ 4} \bigg) = 2 I_0 = \frac{K}{2}\) \(\space14mm\) [Using (i)]

S is equally spaced from s₁ and s₂ according to Young's Double Slit Experiment Derivation. Given that both s₁ and s₂ are derivations of S, they act as two coherent sources. The slits allow light to enter, which then falls on a screen. With respect to the locations of slits s₁ and s₂, this screen is positioned 'D' away. Thomas Young developed the theory of light interference. Two light sources are separated from one another by some distance in the double-slit experiment. Young's double-slit experiment demonstrates that both matter and energy may exhibit wave- and particle-like properties.

The light passes through these slits and falls on the screen that is kept at the distance D from both the slits S₁ and S₂.

• The distance between the two slits is d.
• S₁ is activated.
• S₂ has ended.
• The closed screen is opposite the S₁.
• The screen opposite S₂ is lit.

As a result, an interference pattern appears when slits S₁ and S₂ are both open. The light waves from slits S₁ and S₂ must travel at different distances to reach point P when the slit spacing 'd' and the screen distance D are maintained constant. It suggests that the two slits S₁ and S₂ in the Young double slit experiment have different paths.

Think about two waves that are at different lengths and interfere at point P. Consider two slits, S₁ and S₂, with a monochromatic light source, "S," placed between them at a suitable distance. S₁ and S₂ are equally spaced apart from S. We may thus conclude that S₁ and S₂ are two consistent sources that were descended from S.