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

Answer: (C)

K/2

Answer 2

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.