Question

Derivation of lateral shift

Answer 1

Answer: read the statements and see the image simultaneously

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The shortest (perpendicular) distance between the original direction of the incident ray and the emergent ray is known as the lateral shift.

An incident ray IO is incident on the rectangular glass slab ABCD with an angle of incidence <i from a rarer medium air. As it strikes the point O on the interface of air-glass, it reflects and transmits partially. The transmitted ray OR' bends towards the normal and makes an angle of refraction <r.  The transmitted ray passes straightly through the glass slab until it reaches the point R' on the interface of glass-air. The light bends away from the normal as it emerges out in the air making an angle of emergence <e. The emergent ray and the initial path of the incident ray are parallel to each other as shown in the figure above. The shortest (perpendicular) distance between the incident ray and the emergent ray is known as the lateral shift.

In the figure above, O'R' is the lateral shift.

In a            OO'R',

Sin(i-r)=  

O'R'= sin(i-r) OR'    …………………(i)

Also,  in           ON'R'

Cos(r)=  …………………………..(ii)

Now from expression (i) and (ii),

O'R'=  

O'R'=   ………(iii)  where t' is the thickness of the glass slab.

When the angle of incidence i= 0ο, there is no bending of light as it transmits through glass slab so that <r= 0 degree, hence from expression (iii) O'R'= 0. Similarly, as the angle of incidence is 90 ο, O'N=  =    =  

The variation of lateral shift with the angle of incidence is illustrated by the graph below.

Explanation:

Answer 2

$\large\tt\underline{\red{Answer :-}}$

When a denser medium is kept between two parallel faces inside a rare medium and a ray falls upon one of the two parallel faces reflects into the denser medium and comes out of another surface becoming parallel to the incident ray.

In the successive reflection the deviation at first surface is reversed at second surface but the emergent ray deviates literally.

The distance to what an emergent Ray devited from the direction of incident ray when suffers refraction at two parallel surfaces is called as lateral deviation/ displacement.

The lateral displacement/deviation increase with the increase in

• thickness

• angle of incident

• optical density