Is refractive index inversely proportional to refraction and what will happen if we take a glass filled with kerosene instead of water?
Refraction is how a material responds to light. Refractive index n is the mediating value. Refraction causes the speed of light to change as it travels through the material. The speed in the material is v = c/n, where c is the speed of light in vacuum. Refraction also causes the angle of incident light to change at an interface between two different materials when the light is not perfectly normal to the surface plane.
In summary, when you change the medium from water to kerosene, light will travel at a different speed through the kerosene. Also, when the light beam is not incident at normal to the surface, the light beam will exit at a different physical location on the opposite side of the kerosene filled glass compared to the water filled glass because its refraction angle is different in the two cases.
To address your separate question about proving a lateral shift, please consult standard undergraduate physics textbooks on refraction and Snell's law. Apply these to the physical geometry for the system you are using. Finally, as far as refractive index values for various materials (again, a separate question), material databases can provide insights. Search for such things as high index glass. You might do well to combine your other questions here.
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