Refraction from a glass slab
By Refraction is the bending of light as it passes from one material (medium) to another material with a different refractive index. A glass slab is a rectangular block that produces lateral shift of the incident ray. A glass slab is used to:
Verification of laws of refraction
The direction of refracted ray is given by the laws of refraction:
- The incident ray, refracted ray and the normal (to the interface) lies in the same plane.
- The angle of incidence $i$, the angle of refraction $r$ and the refractive indices are related by Snell's law: \begin{align} \frac{\sin i}{\sin r}=\frac{\mu_2}{\mu_1} \end{align}
- Fix a sheet of paper on a thermocol sheet. Place the glass slab at its middle. Draw the boundary of the slab, and draw a line RP to meet one of the longer boundaries at P, at an angle (say 30 degree). Fix two pins A, B vertically on this line about 10 cm apart. Look at the image of the pins from other side of the slab. Now fix a pin C such that it appears to be in a straight line with the image of A and B. Fix another pin D (at least 10 cm from C) such that all four pins appear to be in straight line.
- Remove the pins and join by a straight line the points where the pins C and D were inserted. Extend this line to meet the boundary of the slab at Q. Join PQ. The lines RP, PQ, and QD represent the directions of the incident ray, the refracted ray within the slab and the emergent ray after the second refraction respectively.
- You will find that the QD is parallel to RP. Also, it is shifted sideways from the direction of RP. Note that the incident ray bent towards the normal at P, as it moved from the optically rarer medium (air) to the optically denser medium (glass). At Q, the ray going from the optically denser medium (glass) to the optically rarer medium (air), bent away from the normal at Q.
- Measure angle of incidence and angle of refraction and calculate \(\mu\).
- Repeat above steps of incident angle of 45 degree and 60 degree.
- You can repeat the experiment, once for the rays passing through the length of the slab and once, through the width. Verify that the lateral shift of the ray is proportional to the thickness of the material of the slab through which the ray passes.
Refractive index using parallax method
The objective is to find refractive index of a glass by measuring real depth $d$ and apparent depth $d^\prime$ of an object placed below the slab. The relation between apparent depth, real depth and refractive index is \begin{align} \mu=\frac{\text{real depth}}{\text{apparent depth}}=\frac{d}{d^\prime} \end{align}
Parallax: If two objects A and B are separated from each other and we see from a position C along line AB, it appears to us that two are touching each other and we are not able to see them as separate objects. However, if we shift our eyes towards left, the two will look separated. If we do not have depth perception, object A will look towards left and B towards right. Similarly, if we shift the eye towards right, the object appears separated, A towards right and B towards left. If the two objects A and B are actually at same place then they always appear in contact wherever we move our eyes.
You need a rectangular glass slab, playing cards, and a scale for this experiment.
- Draw a line on a sheet of paper. Place the paper on a table and put a transparent glass slab over it. The longest side of the slab should be vertical.
- Mark similar line on another paper sheet. Put some blank cards (sheets) on the table adjacent to the slab and on the top of this stack put the marked sheet. Looking from the above, the two lines should be in the same line.
- Insert or remove sheets from the stack to adjust the height so that no PARALLAX remains between the two lines, one as seen through the slab and other on top of the stack. In this situation, the depth of the stack is same as the image of the line formed by the slab.
- Measure the apparent depth $d^\prime$ and real depth $d$ of the line. Calculate the refractive index of the glass by using the formula given above.
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