EXERCISES

A tank is filled with water to a height of $12.5 \mathrm{c}\mathrm{m}$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $9.4 \mathrm{c}\mathrm{m}$. What is the refractive index of water? If water is replaced by a liquid of refractive index $1.63$ up to the same height, by what distance would the microscope have to be moved to focus on the needle again?

A diver under water, looks obliquely at a fisherman standing on the bank of a lake. Would the fisherman look taller or shorter to the diver than what he actually is?

Does the apparent depth of a tank of water change if viewed obliquely? If so, does the apparent depth increase or decrease?
 

The refractive index of diamond is much greater than that of ordinary glass. Is this fact of some use to a diamond cutter?

In viewing through a magnifying glass, one usually positions one’s eyes very close to the lens. Does angular magnification change if the eye is moved back?

Magnifying power of a simple microscope is inversely proportional to the focal length of the lens. What then stops us from using a convex lens of smaller and smaller focal length and achieving greater and greater magnifying power?

Why must both the objective and the eyepiece of a compound microscope have short focal lengths?

When viewing through a compound microscope, our eyes should be positioned not on the eyepiece but a short distance away from it for best viewing. Why? How much should be that short distance between the eye and eyepiece?