A slit of width $$a$$ is illuminated by red light of wavelength $$6500 \mathop A\limits^o$$. If the first diffraction minimum falls at $$30^{\circ}$$, then the value of $$a$$ is

Which of the following statements are correct with reference to single slit diffraction pattern?

(I) Fringes are of unequal width.

(II) Fringes are of equal width.

(III) Light energy is conserved.

(IV) Intensities of all bright fringes are equal.

In the Young's double slit experiment a monochromatic source of wavelength $$\lambda$$ is used. The intensity of light passing through each slit is $$I_0$$. The intensity of light reaching the screen $$S_C$$ at a point $$P$$, a distance $$x$$ from $$O$$ is given by (Take, $$d<< D$$)

Three polaroid sheets $$P_1, P_2$$ and $$P_3$$ are kept parallel to each other such that the angle between pass axes of $$P_1$$ and $$P_2$$ is $$45^{\circ}$$ and that between $$P_2$$ and $$P_3$$ is $$45^{\circ}$$. If unpolarised beam of light of intensity $$128 \mathrm{~Wm}^{-2}$$ is incident on $$P_1$$. What is the intensity of light oming out of $$P_3$$ ?