Question

In young’s double slit experiment the intensity of light at a point on the screen where the path difference is is K. The intensity of light at a point where the path difference is [ is the wave length of light used] is

Answer 1

The condition of the problem is:

In young’s double slit experiment the intensity of light at a point on the screen where the path difference is λ is K. The intensity of light at a point where the path difference is λ/4 is...

Solution

For path difference of one wavelength, the phase difference is

$$\phi_1=\frac{2\pi}{\lambda}x=\frac{2\pi}{\lambda}\lambda=2\pi.$$

For x=λ/4 the phase difference is

$$\phi_2=\frac{2\pi}{\lambda}x=\frac{2\pi}{\lambda}\frac{\lambda}{4}=\frac{\pi}{2}.$$

The intensity of light is

$$I=K\text{ cos}^2\bigg(\frac{\phi}{2}\bigg).$$

Therefore,

$$I_1=K, \\I_2=K\text{ cos}^2\bigg(\frac{\pi/2}{2}\bigg)=\frac{K}{2}.$$