Index of Refraction of the block

Draw a line on a piece of paper and put the block on it as in the figure (the figure is a view from above).

Now shine the laser beam into the block at some angle from perpendicular to the edge. Measure the angle of incidence and the angle of refraction:

Then you can determine the index of refraction since:

nincsinθinc = nrefrsinθrefr

The index of refraction of air (ninc), is 1.000293, and so it can be taken to be 1.

Total Internal Reflection

As the angle of incidence is increased, eventually it will approach 90º. Beyond this, the beam obviously cannot enter the block. The angle of refraction for θinc = 90 can be determined by:

nincsin(90º) = nrefrsinθrefr

(1)(1) = nrefrsinθrefr

sinθrefr = 1/nrefr

θrefr = arcsin(1/nrefr)

Calculate this.

For a beam coming out of the block into the air, this is the maximum angle that it can have from the line perpendicular to the edge of the block and still send some photons out of the block. For angles larger than this, all photons are internally reflected.

Now measure θrefr. The best way to do this is by using the convex lens as in the figure below:

Simply adjust the angle of the beam until the exiting part is about tangent to the curved lens surface. At angles steeper than this, all the light is reflected back to the interior of the lens. It might help here to draw another line perpendicular to the one already on the paper, one that will be tangent to the edge of the lens, so that you can be more sure that you're measuring your refraction angle properly.

Focal Length of the Convex Lens

Now measure the focal length of the convex lens. To do this, send several parallel beams through the lens and see where they converge. One way to make 2 parallel beams is depicted in the figure below:

Measure the focal length from the focal point to the flat surface of the lens.

Focal Length of the Diverging Lens

Use the same setup to measure the focal length of the diverging lens. Two parallel beams won't go through the focal point, but if you trace their paths backwards through the lens, they'll meet at one of the focal points.

Focal Length of the Concave Mirror

Use the same method to find the focal length of the concave mirror.