As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of the material for both the lenses is 1.75. Both the lenses are placed at distance of 40 cm from each other. Due to the combination, the image of the object is formed at distance $$x=$$ _________ cm, from concave lens.

Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is $$\pi$$. The difference of resultant intensities, at the point A and B, will be _________ I.

The X-Y plane be taken as the boundary between two transparent media $$\mathrm{M}_{1}$$ and $$\mathrm{M}_{2}$$. $$\mathrm{M}_{1}$$ in $$Z \geqslant 0$$ has a refractive index of $$\sqrt{2}$$ and $$M_{2}$$ with $$Z<0$$ has a refractive index of $$\sqrt{3}$$. A ray of light travelling in $$\mathrm{M}_{1}$$ along the direction given by the vector $$\overrightarrow{\mathrm{P}}=4 \sqrt{3} \hat{i}-3 \sqrt{3} \hat{j}-5 \hat{k}$$, is incident on the plane of separation. The value of difference between the angle of incident in $$\mathrm{M}_{1}$$ and the angle of refraction in $$\mathrm{M}_{2}$$ will be __________ degree.

An object 'O' is placed at a distance of $$100 \mathrm{~cm}$$ in front of a concave mirror of radius of curvature $$200 \mathrm{~cm}$$ as shown in the figure. The object starts moving towards the mirror at a speed $$2 \mathrm{~cm} / \mathrm{s}$$. The position of the image from the mirror after $$10 \mathrm{~s}$$ will be at _________ $$\mathrm{cm}$$.