Optical lever, how to find the radius of curvature and refractive index of a convex lens.

Now, we all can find out the focal length of a lens, but how do we find out the radius of curvature of the lens as well as the refractive index of the lens? Well, it turns out it is very easy. 

What we need:

1. A small plane mirror (preferred size < 2 cm by 3 cm) with a stand as shown below. Remember that all the legs have to be of the same length.
   
2. A lens
3. A plane glass slab
4. A telescope 
5. A meter scale
6. A lamp 
7. A stand to hold the meter scale upright
8. A stand to keep the lens, mirror and slab to a reasonable distance above the ground.( a table or bunch of books should do the job, remember that they should be leveled properly and the lens, mirror and slab should be kept at the edge of the table or books)

What to do:

1. If you are using a standard laboratory round table stand, keep in mind that it is properly leveled. 
2. Once everything is leveled, arrange everything as follows
   
3. Now level the mirror properly so that after focusing the telescope on the mirror, we can see the scale properly.
4. Once you see the scale in the mirror through the telescope, take the readings of the left side and the right side of the scale. First balance the mirror on the front legs and take the readings then balance them on the hind legs and take the readings. Record them as shown in the observations part.
5. Now, once you have recorded the readings for glass slab, put the lens in between the glass slab and the mirror arrangement, i.e keep the lens on top of the glass slab and put the mirror arrangement on top.
   
6. Now do the same as you did for the glass slab, i.e. take readings for the front legs and the hind legs for one curved side. Then, once done, flip the lens and take the readings for the second curved side.
7. Now, we need to find the focal length of the lens. Its very easy. Take a meter scale and put it perpendicularly on the wall just opposite to the window (note there should be a bright source of light where the scale is pointing). Now put the lens on the scale and see where the image (of the bright object or your window) is the sharpest and see where you need to keep the lens to get the sharpest image. Record the distance between the lens and the wall. this is the focal length of your lens.

Observation:

1. Distance between the front and hind leg= 2a =_______cm .Hence a=_______cm
2. Distance between the middle legs= 2b =_______cm .Hence b=______cm
3. Distance between the scale and the mirror=L=_______cm
4. Observation table:
   
5. Now apply the above formula of focal length, substitute all the values and interchange to get the refractive index i.

Result:

For convex lens:

1. The radius of curvature of surface one is=R1=________cm.
2. The radius of curvature of surface tow is=R2=________cm.
3. The refractive index of the lens is =i=________.

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