Question

on what factors does the value of lateral shift depends?​

Answer 1

Let be the path of the ray of light, as shown in the figure.

The path that the ray would have taken had it not been refracted is .

The lateral shift is the perpendicular distance between the path of the ray of light when it emerges from the refracting medium and the path that the ray would have taken had it not been refracted.

⇒ The lateral shift is , where ⊥.

The angle of incidence is and the angle of refraction is .

⇒=sin(∠)=sin(−).

Let the thickness of the glass slab, be .

⇒=cos=cos.

⇒=(cos)sin(−)=(cos)(sincos−cossin)

=(sin−costan).

sinsin=, the refractive index.

⇒sin=sin.

⇒tan=sin2−sin2√.

⇒=(sin−cossin2−sin2√)=(sin−sin222−sin2√).

⇒ The variance of the lateral shift with the angle of incidence is given by the formula,

Lateral shift  =(sin−sin222−sin2√).

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