A needle is lying at the bottom of a water tank of height 12 cm. The apparent depth of the needle measured by a microscope is 9 cm . If the water is replaced by a liquid of refractive index of 1.5 of same height, the distance through which the microscope has to be moved to focus the needle again is

The radii of curvature of a double convex lens are 4 cm and 8 cm . If the refractive index of the material of the lens is 1.5 , the focal length of the lens is nearly.

A ray is incident from a medium of refractive index 2 into a medium of refractive index 1. The critical angle is

Light of wavelength $$300 \mathrm{~nm}$$ in medium $$A$$ enters into medium $$B$$ through a plane surface. If the frequency of light is $$5 \times 10^{14} \mathrm{~Hz}$$ and the ratio of speed in medium $$A$$ to that in medium $$B$$ is $$4 / 5$$, the absolute refractive index of medium $$B$$ is