Question

Obtain the equation for lateral displacement of light passing through a glass slab.

Answer 1

1. When a ray of light passes through a glass slab it refracts at two refracting surfaces.
2. When the light ray enters the slab it travels from a rarer medium (air) to a denser medium (glass), results in deviation of ray towards the normal. When the light ray leaves the slab it travels from denser medium to rarer medium resulting in deviation of ray away from the normal.
   
   Refraction in glass slab
3. After the two refractions, the emerging ray has the same direction as that of the incident ray on the slab with a lateral displacement or shift L.
4. Consider a glass slab of thickness and refractive index n is kept in air medium.
5. In the right angle triangle ∆ BCE,
   sin (i – r) = `"L"/"BC"`;
   BC = `"L"/(sin ("i - r"))`   ....(1)
6. In the right angle triangle ∆ BCF, ....(2)
   cos(r) = `"t"/"BC"`;
   BC = `"t"/(cos ("r"))`
   Equating equations (1) & (2)
   `"L"/(sin ("i - r")) = "t"/(cos ("r"))`
7. After rearranging,
   L = `"t" [(sin ("i - r"))/(cos ("r"))]`