Q45P - University Physics with Modern Physics

Question

You sight along the rim of a glass with vertical sides so that the top rim is lined up with the opposite edge of the bottom (Fig. P33.45a). The glass is  =thin-walled, hollow cylinder  high. The diameter of the top and bottom of the glass is  While you keep your eye in the same position, a friend fills the glass with a transparent liquid, and you then see a dime that is lying at the center of the bottom of the glass (Fig. P33.45b). What is the index of refraction of the liquid?

Step-by-Step Solution

Answer

the index of refraction of liquid will be 1.84

Step 1 : About Index of refraction

The index of refraction, n, is the ratio of the speed of light in a vacuum, c, to the speed of light in a medium, c': One consequence of this difference in speed is that when light goes from one medium to another at an angle, the propagation vector in the new medium has a different angle with respect to the normal.

Step 2: Determine the index of refraction for liquid

Before pouring the liquid into the glass we have the angle of ray as shoWn below:\                                  

For the second part where glass is filled with the liquid, we have the 05 :

 

Now apply the Snell's Law for the above case- Assume we have the index of refraction of liquid equal to n- We know that

index of refraction of air is equal to 1-

 

Hence, the index of refraction of liquid will be 1.84-