In Young's double slit experiment, the wavelength of light used is '$$\lambda$$'. The intensity at a point is '$$\mathrm{I}$$' where path difference is $$\left(\frac{\lambda}{4}\right)$$. If $$I_0$$ denotes the maximum intensity, then the ratio $$\left(\frac{\mathrm{I}}{\mathrm{I}_0}\right)$$ is

$$\left(\sin \frac{\pi}{4}=\cos \frac{\pi}{4}=\frac{1}{\sqrt{2}}\right)$$

In Young's double slit experiment, the fringe width is $$2 \mathrm{~mm}$$. The separation between the $$13^{\text {th }}$$ bright fringe and the $$4^{\text {th }}$$ dark fringe from the centre of the screen on same side will be

A beam of unpolarized light passes through a tourmaline crystal A and then it passes through a second tourmaline crystal B oriented so that its principal plane is parallel to that of A. The intensity of emergent light is $$I_0$$. Now B is rotated by $$45^{\circ}$$ about the ray. The emergent light will have intensity $$\left(\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)$$

In a diffraction pattern due to single slit of width '$$a$$', the first minimum is observed at an angle of $$30^{\circ}$$ when the light of wavelength $$5400 \mathop A\limits^o$$ is incident on the slit. The first secondary maximum is observed at an angle of $$\left(\sin 30^{\circ}=\frac{1}{2}\right)$$