A ray of light is incident from air on a glass plate having thickness $$\sqrt3$$ cm and refractive index $$\sqrt2$$. The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is ____________ $$\times$$ 10$$^{-2}$$ cm. (given $$\sin 15^\circ = 0.26$$)

A convex lens of refractive index 1.5 and focal length 18cm in air is immersed in water. The change in focal length of the lens will be ___________ cm.

(Given refractive index of water $$=\frac{4}{3}$$)

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.

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.