How Do You Calculate Refraction Index and Object Distance in Optics Problems?

[Saturnfirefly]

Homework Statement

1. When light travels from a material to air, total reflection occurs beyond 54 degrees. Calculate the index of refraction.

2. A converging lens has a focal length of 20 cm. When an object is placed at a certain disctance from the lens, a virtual image is created. How far from the lens is the object placed if the height of the image is 4 times greater than the object?

Homework Equations

1. sinC= n2/n1

2. ?

The Attempt at a Solution

1. I can use the equation, but I don't know how to calculate(?) the critical angle. I don't think any calculating is neccesary. The critical angle should be 45 (I'm not totaly sure) degrees, and my question is why?

2. I know that you have to place the object within the focal point to get a virtual image using a converging lens. And that tells us that the answer should be -something. But I don't know how to solve the equation... anyone that can by detail show me how to solve it? Answer should be di = -60

 

[Doc Al]

1) The critical angle is given. Use it to solve for the index of refraction.
2) If the image is 4x bigger than the object, what does that tell you about the ratio of object and image distances? (Look up magnification.)

 

[timon]

the critical angle is 54 degrees, not 45, or am i missing something here?

use the formula for the critical angle to calculate the index of refraction(sin critical angle = 1/refraction index)