In a Young's double slit experiment the intensity at a point where the path difference is $${\lambda \over 6}$$ ( $$\lambda $$ being the wavelength of light used ) is $$I$$. If $${I_0}$$ denotes the maximum intensity, $${I \over {{I_0}}}$$ is equal to

Two lenses of power $$-15$$ $$D$$ and $$+5$$ $$D$$ are in contact with each other. The focal length of the combination is

The refractive index of a glass is $$1.520$$ for red light and $$1.525$$ for blue light. Let $${D_1}$$ and $${D_2}$$ be angles of minimum deviation for red and blue light respectively in a prism of this glass. Then,

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $${4 \over 3}$$ and the fish is $$12$$ $$cm$$ below the surface, the radius of this circle in $$cm$$ is