A student measures the focal length of a convex lens by putting an object pin at a distance $$'u'$$ from the lens and measuring the distance $$'v'$$ of the image pin. The graph between $$'u'$$ and $$'v'$$ plotted by the student should look like

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