Question

how does lateral shift change with the increase in angle

Answer 1

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

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 CF,CF, where CF⊥BE.CF⊥BE.

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

⇒CF=BCsin(∠CBF)=BCsin(i−r).⇒CF=BCsin⁡(∠CBF)=BCsin⁡(i−r).

Let the thickness of the glass slab, BGBG be t.t.

⇒BC=BGcosr=tcosr.⇒BC=BGcos⁡r=tcos⁡r.

⇒CF=(tcosr)sin(i−r)=(tcosr)(sinicosr−cosisinr)⇒CF=(tcos⁡r)sin⁡(i−r)=(tcos⁡r)(sin⁡icos⁡r−cos⁡isin⁡r)

=t(sini−cositanr).=t(sin⁡i−cos⁡itan⁡r).

sinisinr=μ,sin⁡isin⁡r=μ, the refractive index.

⇒sinr=siniμ.⇒sin⁡r=sin⁡iμ.

⇒tanr=siniμ2−sin2i√.⇒tan⁡r=sin⁡iμ2−sin2⁡i.

⇒CF=t(sini−cosisiniμ2−sin2i√)=t(sini−sin2i2μ2−sin2i√).⇒CF=t(sin⁡i−cos⁡isin⁡iμ2−sin2⁡i)=t(sin⁡i−sin⁡2i2μ2−sin2⁡i).

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

 Lateral shift =t(sini−sin2i2μ2−sin2i√).

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